Valentin Nikolaevich Rudenko shares the story of his visit to the city of Cascina (Italy), where he spent a week on the then newly built “gravitational antenna” - optical interferometer Michelson. On the way to the destination, the taxi driver asks why the installation was built. “People here think it’s for talking to God,” the driver admits.

– What are gravitational waves?

– The gravitational wave is one of the “carriers of astrophysical information.” There are visible channels of astrophysical information; telescopes play a special role in “distant vision”. Astronomers have also mastered low-frequency channels - microwave and infrared, and high-frequency channels - X-ray and gamma. In addition to electromagnetic radiation, we can detect streams of particles from Space. For this purpose, neutrino telescopes are used - large-sized detectors of cosmic neutrinos - particles that weakly interact with matter and are therefore difficult to register. Almost all theoretically predicted and laboratory-studied types of “carriers of astrophysical information” have been reliably mastered in practice. The exception was gravity - the most weak interaction in the microcosm and the most powerful force in the macrocosm.

Gravity is geometry. Gravitational waves are geometric waves, that is, waves that change the geometric characteristics of space when they pass through that space. Roughly speaking, these are waves that deform space. Strain is the relative change in the distance between two points. Gravitational radiation differs from all other types of radiation precisely in that it is geometric.

– Did Einstein predict gravitational waves?

– Formally, it is believed that gravitational waves were predicted by Einstein as one of the consequences of his general theory relativity, but in fact their existence becomes obvious already in the special theory of relativity.

The theory of relativity suggests that due to gravitational attraction, gravitational collapse is possible, that is, an object being pulled together as a result of collapse, roughly speaking, to a point. Then the gravity is so strong that light cannot even escape from it, so such an object is figuratively called a black hole.

– What is the peculiarity of gravitational interaction?

A feature of gravitational interaction is the principle of equivalence. According to it, the dynamic response of a test body in a gravitational field does not depend on the mass of this body. Simply put, all bodies fall with the same acceleration.

Gravitational interaction is the weakest we know today.

– Who was the first to try to catch a gravitational wave?

– The gravitational wave experiment was first conducted by Joseph Weber from the University of Maryland (USA). He created a gravitational detector, which is now kept in the Smithsonian Museum in Washington. In 1968-1972, Joe Weber conducted a series of observations on a pair of spatially separated detectors, trying to isolate cases of "coincidences". The coincidence technique is borrowed from nuclear physics. Low statistical significance gravitational signals received by Weber caused a critical attitude towards the results of the experiment: there was no confidence that it was possible to detect gravitational waves. Subsequently, scientists tried to increase the sensitivity of Weber-type detectors. It took 45 years to develop a detector whose sensitivity was adequate to the astrophysical forecast.

During the start of the experiment, many other experiments took place before fixation; impulses were recorded during this period, but their intensity was too low.

– Why was the signal fixation not announced immediately?

– Gravitational waves were recorded back in September 2015. But even if a coincidence was recorded, before announcing it, it is necessary to prove that it is not random. The signal taken from any antenna always contains noise bursts (short-term bursts), and one of them can accidentally occur simultaneously with a noise burst on another antenna. It is possible to prove that the coincidence did not occur by chance only with the help of statistical estimates.

– Why are discoveries in the field of gravitational waves so important?

– The ability to register the relict gravitational background and measure its characteristics, such as density, temperature, etc., allows us to approach the beginning of the universe.

What's attractive is that gravitational radiation is difficult to detect because it interacts very weakly with matter. But, thanks to this same property, it passes without absorption from the objects most distant from us with the most mysterious, from the point of view of matter, properties.

We can say that gravitational radiation passes without distortion. The most ambitious goal is to study the gravitational radiation that was separated from the primordial matter in the Big Bang Theory, which was created at the creation of the Universe.

– Does the discovery of gravitational waves rule out quantum theory?

The theory of gravity assumes the existence of gravitational collapse, that is, the contraction of massive objects to a point. At the same time, the quantum theory developed by the Copenhagen School suggests that, thanks to the uncertainty principle, it is impossible to simultaneously indicate exactly such parameters as the coordinate, speed and momentum of a body. There is an uncertainty principle here; it is impossible to determine the exact trajectory, because the trajectory is both a coordinate and a speed, etc. It is only possible to determine a certain conditional confidence corridor within the limits of this error, which is associated with the principles of uncertainty. Quantum theory categorically denies the possibility of point objects, but describes them in a statistically probabilistic manner: it does not specifically indicate coordinates, but indicates the probability that it has certain coordinates.

The question of unifying quantum theory and the theory of gravity is one of the fundamental questions of creating a unified field theory.

They continue to work on it now, and the words “quantum gravity” mean a completely advanced area of ​​science, the border of knowledge and ignorance, where all the theorists in the world are now working.

– What can the discovery bring in the future?

Gravitational waves must inevitably lie in the foundation modern science as one of the components of our knowledge. They are given significant role in the evolution of the Universe and with the help of these waves the Universe should be studied. Discovery promotes general development science and culture.

If you decide to go beyond the scope of today's science, then it is permissible to imagine gravitational telecommunication lines, jet devices using gravitational radiation, gravitational-wave introscopy devices.

– Do gravitational waves have anything to do with extrasensory perception and telepathy?

Dont Have. The described effects are the effects of the quantum world, the effects of optics.

Interviewed by Anna Utkina

Gravitational waves, theoretically predicted by Einstein back in 1917, are still awaiting their discoverer.

At the end of 1969, University of Maryland physics professor Joseph Weber made a sensational statement. He announced that he had discovered gravitational waves coming to Earth from the depths of space. Until that time, no scientist had made such claims, and the very possibility of detecting such waves was considered far from obvious. However, Weber was known as an authority in his field, and therefore his colleagues took his message very seriously.

However, disappointment soon set in. The amplitudes of the waves allegedly recorded by Weber were millions of times higher than the theoretical value. Weber argued that these waves came from the center of our Galaxy, obscured by dust clouds, about which little was then known. Astrophysicists have suggested that there is a giant black hole hiding there, which annually devours thousands of stars and throws out part of the absorbed energy in the form of gravitational radiation, and astronomers began a futile search for more obvious traces of this cosmic cannibalism (it has now been proven that there really is a black hole there, but it leads behave quite decently). Physicists from the USA, USSR, France, Germany, England and Italy began experiments on detectors of the same type - and achieved nothing.

Scientists still don’t know what to attribute the strange readings from Weber’s instruments. However, his efforts were not in vain, although gravitational waves have still not been detected. Several installations to search for them have already been built or are being built, and in ten years such detectors will be launched into space. It is quite possible that in the not too distant future, gravitational radiation will become as observable a physical reality as electromagnetic oscillations. Unfortunately, Joseph Weber will no longer know this - he died in September 2000.

What are gravitational waves

It is often said that gravitational waves are disturbances of the gravitational field propagating in space. This definition is correct, but incomplete. According to the general theory of relativity, gravity arises due to the curvature of the space-time continuum. Gravity waves are fluctuations of the space-time metric, which manifest themselves as oscillations gravitational field, which is why they are often figuratively called space-time ripples. Gravitational waves were theoretically predicted in 1917 by Albert Einstein. No one doubts their existence, but gravitational waves are still waiting for their discoverer.

The source of gravitational waves is any movement of material bodies that leads to a non-uniform change in the force of gravity in the surrounding space. Moving with constant speed the body does not radiate anything, since the nature of its gravitational field does not change. To emit gravitational waves, accelerations are necessary, but not just any acceleration. A cylinder that rotates around its axis of symmetry experiences acceleration, but its gravitational field remains uniform and gravitational waves do not arise. But if you spin this cylinder around a different axis, the field will begin to oscillate, and gravitational waves will run from the cylinder in all directions.

This conclusion applies to any body (or system of bodies) that is asymmetrical about the axis of rotation (in such cases the body is said to have a quadrupole moment). A mass system whose quadrupole moment changes with time always emits gravitational waves.

Basic properties of gravitational waves

Astrophysicists suggest that it is the radiation of gravitational waves, taking away energy, that limits the speed of rotation of a massive pulsar when absorbing matter from a neighboring star.


Gravity beacons of space

Gravitational radiation from terrestrial sources is extremely weak. A steel column weighing 10,000 tons, suspended from the center in a horizontal plane and spun around a vertical axis up to 600 rpm, emits a power of approximately 10 -24 W. Therefore, the only hope of detecting gravitational waves is to find a cosmic source of gravitational radiation.

In this regard, close double stars are very promising. The reason is simple: the power of gravitational radiation of such a system grows in inverse proportion to the fifth power of its diameter. It is even better if the trajectories of the stars are very elongated, since this increases the rate of change of the quadrupole moment. It is quite good if the binary system consists of neutron stars or black holes. Such systems are similar to gravitational beacons in space - their radiation is periodic.

There are also “pulse” sources in space that generate short but extremely powerful gravitational bursts. This happens when a massive star collapses before a supernova explosion. However, the star's deformation must be asymmetric, otherwise the radiation will not occur. During collapse, gravitational waves can carry away up to 10% of the total energy of the star! The power of gravitational radiation in this case is about 10 50 W. Even more energy is released during the merger of neutron stars, here the peak power reaches 10 52 W. An excellent source of radiation is the collision of black holes: their masses can exceed the masses of neutron stars by billions of times.

Another source of gravitational waves is cosmological inflation. Right after big bang The Universe began to expand extremely quickly, and in less than 10 -34 seconds its diameter increased from 10 -33 cm to its macroscopic size. This process immeasurably strengthened the gravitational waves that existed before it began, and their descendants persist to this day.

Indirect confirmations

The first evidence of the existence of gravitational waves comes from the work of American radio astronomer Joseph Taylor and his student Russell Hulse. In 1974, they discovered a pair of neutron stars orbiting each other (a radio-emitting pulsar with a silent companion). The pulsar rotated around its axis with a stable angular velocity (which is not always the case) and therefore served as an extremely accurate clock. This feature made it possible to measure the masses of both stars and determine the nature of their orbital motion. It turned out that the orbital period of this binary system (about 3 hours 45 minutes) is reduced by 70 μs annually. This value agrees well with the solutions of the equations of the general theory of relativity, which describe the loss of energy of a stellar pair due to gravitational radiation (however, the collision of these stars will not happen soon, after 300 million years). In 1993, Taylor and Hulse were awarded the Nobel Prize for this discovery.

Gravity wave antennas

How to detect gravitational waves experimentally? Weber used meter-long solid aluminum cylinders with piezoelectric sensors at the ends as detectors. They were isolated with maximum care from external mechanical influences in a vacuum chamber. Weber installed two of these cylinders in a bunker under the University of Maryland golf course, and one at Argonne National Laboratory.

The idea of ​​the experiment is simple. Space is compressed and stretched under the influence of gravitational waves. Thanks to this, the cylinder vibrates in the longitudinal direction, acting as a gravitational wave antenna, and piezoelectric crystals convert the vibrations into electrical signals. Any passage of cosmic gravitational waves almost simultaneously affects detectors separated by a thousand kilometers, which makes it possible to filter gravitational impulses from various types of noise.

Weber's sensors were able to detect displacements of the ends of the cylinder equal to only 10 -15 of its length - in this case 10 -13 cm. It was precisely such fluctuations that Weber was able to detect, which he first reported in 1959 on the pages Physical Review Letters. All attempts to repeat these results have been futile. Weber's data also contradicts the theory, which practically does not allow us to expect relative displacements above 10 -18 (and values ​​​​less than 10 -20 are much more likely). It is possible that Weber made a mistake when statistically processing the results. The first attempt to experimentally detect gravitational radiation ended in failure.

Subsequently, gravitational wave antennas were significantly improved. In 1967, American physicist Bill Fairbank proposed cooling them in liquid helium. This not only made it possible to get rid of most of the thermal noise, but also opened up the possibility of using SQUIDs (superconducting quantum interferometers), the most accurate ultra-sensitive magnetometers. The implementation of this idea turned out to be fraught with many technical difficulties, and Fairbank himself did not live to see it. By the early 1980s, physicists from Stanford University had built an installation with a sensitivity of 10 -18, but no waves were detected. Now in a number of countries there are ultra-cryogenic vibration detectors of gravitational waves operating at temperatures only tenths and hundredths of a degree above absolute zero. This is, for example, the AURIGA installation in Padua. The antenna for it is a three-meter cylinder made of aluminum-magnesium alloy, the diameter of which is 60 cm and the weight is 2.3 tons. It is suspended in a vacuum chamber cooled to 0.1 K. Its shocks (with a frequency of about 1000 Hz) are transmitted to an auxiliary resonator weighing 1 kg, which vibrates with the same frequency, but with a much larger amplitude. These vibrations are recorded by measuring equipment and analyzed using a computer. The sensitivity of the AURIGA complex is about 10 -20 -10 -21.

Interferometers

Another method for detecting gravitational waves is based on the abandonment of massive resonators in favor of light rays. It was first proposed by Soviet physicists Mikhail Herzenstein and Vladislav Pustovoit in 1962, and two years later by Weber. In the early 1970s, an employee research laboratory corporations Hughes Aircraft Robert Forward (a former Weber graduate student, later a very famous science fiction writer) built the first such detector with quite decent sensitivity. Then a professor at the Massachusetts Institute of Technology(MIT) Rainer Weiss performed a very in-depth theoretical analysis of the possibilities of detecting gravitational waves using optical methods.

These methods involve the use of analogues of the device with which 125 years ago physicist Albert Michelson proved that the speed of light is strictly the same in all directions. In this installation, a Michelson interferometer, a beam of light hits a translucent plate and is divided into two mutually perpendicular beams, which are reflected from mirrors located at the same distance from the plate. Then the beams merge again and fall on the screen, where an interference pattern appears (light and dark stripes and lines). If the speed of light depends on its direction, then when the entire installation is rotated, this picture should change; if not, it should remain the same as before.

The gravitational wave interference detector works in a similar way. A passing wave deforms space and changes the length of each arm of the interferometer (the path along which light travels from the splitter to the mirror), stretching one arm and compressing the other. The interference pattern changes, and this can be registered. But this is not easy: if the expected relative change in the length of the arms of the interferometer is 10 -20, then with a tabletop size of the device (like Michelson's) it results in oscillations with an amplitude of the order of 10 -18 cm. For comparison: visible light waves are 10 trillion times longer! You can increase the length of the shoulders to several kilometers, but problems will still remain. The laser light source must be both powerful and stable in frequency, the mirrors must be perfectly flat and perfectly reflective, the vacuum in the pipes through which the light travels must be as deep as possible, and the mechanical stabilization of the entire system must be truly perfect. In short, a gravitational wave interference detector is an expensive and bulky device.

Today the largest installation of this kind is the American LIGO complex (Light Interferometer Gravitational Waves Observatory). It consists of two observatories, one of which is located on the Pacific coast of the United States, and the other near Gulf of Mexico. Measurements are made using three interferometers (two in Washington state, one in Louisiana) with four-kilometer-long arms. The installation is equipped with mirror light accumulators, which increase its sensitivity. “Since November 2005, all three of our interferometers have been operating normally,” LIGO complex representative Peter Solson, a professor of physics at Syracuse University, told Popular Mechanics. - We constantly exchange data with other observatories trying to detect gravitational waves with a frequency of tens and hundreds of hertz, which arose during the most powerful supernova explosions and mergers of neutron stars and black holes. Currently in operation is the German GEO 600 interferometer (arm length - 600 m), located 25 km from Hannover. The 300-meter Japanese TAMA instrument is currently being upgraded. The three-kilometer Virgo detector near Pisa will join the effort in early 2007, and at frequencies below 50 Hz it will be able to surpass LIGO. Installations with ultracryogenic resonators operate with increasing efficiency, although their sensitivity is still somewhat less than ours.”

Prospects

What does the near future hold for gravitational wave detection methods? Professor Rainer Weiss told Popular Mechanics about this: “In a few years, more powerful lasers and more advanced detectors will be installed in the observatories of the LIGO complex, which will lead to a 15-fold increase in sensitivity. Now it is 10 -21 (at frequencies of about 100 Hz), and after modernization it will exceed 10 -22. The upgraded complex, Advanced LIGO, will increase the depth of penetration into space by 15 times. Moscow State University professor Vladimir Braginsky, one of the pioneers in the study of gravitational waves, is actively involved in this project.

The launch of the LISA space interferometer is planned for the middle of the next decade ( Laser Interferometer Space Antenna) with an arm length of 5 million kilometers, it is a joint project of NASA and the European Space Agency. The sensitivity of this observatory will be hundreds of times higher than the capabilities of ground-based instruments. It is primarily designed to search for low-frequency (10 -4 -10 -1 Hz) gravitational waves, which cannot be detected on the Earth's surface due to atmospheric and seismic interference. Such waves are emitted by double star systems, quite typical inhabitants of the Cosmos. LISA will also be able to detect gravitational waves generated when ordinary stars are absorbed by black holes. But to detect relict gravitational waves that carry information about the state of matter in the first moments after the Big Bang, more advanced space instruments will most likely be required. Such an installation Big Bang Observer, is currently being discussed, but it is unlikely that it will be created and launched earlier than in 30-40 years.”

The first direct detection of gravitational waves was revealed to the world on February 11, 2016 and generated headlines around the world. For this discovery in 2017, physicists received Nobel Prize and officially launched new era gravitational astronomy. But a team of physicists at the Niels Bohr Institute in Copenhagen, Denmark, question the finding, based on their own independent analysis of the data over the past two and a half years.

One of the most mysterious objects in history, black holes, regularly attract attention. We know that they collide, merge, change brightness, and even evaporate. And also, in theory, black holes can connect Universes with each other using . However, all our knowledge and assumptions about these massive objects may turn out to be inaccurate. Recently in scientific community Rumors have emerged that scientists have received a signal emanating from a black hole, the size and mass of which is so enormous that its existence is physically impossible.

The first direct detection of gravitational waves was revealed to the world on February 11, 2016 and generated headlines around the world. For this discovery, physicists received the Nobel Prize in 2017 and officially launched a new era of gravitational astronomy. But a team of physicists at the Niels Bohr Institute in Copenhagen question the finding, based on their own independent analysis of the data over the past two and a half years.

Gravitational waves - artist's rendering

Gravitational waves are disturbances of the space-time metric that break away from the source and propagate like waves (the so-called “space-time ripples”).

In general relativity and most others modern theories In gravity, gravitational waves are generated by the motion of massive bodies with variable acceleration. Gravitational waves propagate freely in space at the speed of light. Due to the relative weakness gravitational forces(compared to others) these waves have a very small magnitude, which is difficult to register.

Polarized gravitational wave

Gravitational waves are predicted by the general theory of relativity (GR), and many others. They were first directly detected in September 2015 by two twin detectors, which detected gravitational waves, likely resulting from the merger of two and the formation of one more massive rotating black hole. Indirect evidence of their existence has been known since the 1970s - General Relativity predicts the rate of convergence of close systems due to the loss of energy due to the emission of gravitational waves, which coincides with observations. Direct registration of gravitational waves and their use to determine the parameters of astrophysical processes is an important task of modern physics and astronomy.

Within the framework of general relativity, gravitational waves are described by solutions of wave-type Einstein equations, which represent a perturbation of the space-time metric moving at the speed of light (in the linear approximation). The manifestation of this disturbance should be, in particular, a periodic change in the distance between two freely falling (that is, not influenced by any forces) test masses. Amplitude h gravitational wave is a dimensionless quantity - a relative change in distance. The predicted maximum amplitudes of gravitational waves from astrophysical objects (for example, compact binary systems) and phenomena (explosions, mergers, captures by black holes, etc.) when measured are very small ( h=10 −18 -10 −23). A weak (linear) gravitational wave, according to the general theory of relativity, transfers energy and momentum, moves at the speed of light, is transverse, quadrupole and is described by two independent components located at an angle of 45° to each other (has two directions of polarization).

Different theories predict the speed of propagation of gravitational waves differently. In general relativity, it is equal to the speed of light (in the linear approximation). In other theories of gravity, it can take any value, including infinity. According to the first registration of gravitational waves, their dispersion turned out to be compatible with a massless graviton, and the speed was estimated to be equal to the speed of light.

Generation of gravitational waves

A system of two neutron stars creates ripples in space-time

A gravitational wave is emitted by any matter moving with asymmetric acceleration. For a wave of significant amplitude to occur, an extremely large mass of the emitter and/or enormous accelerations are required; the amplitude of the gravitational wave is directly proportional first derivative of acceleration and the mass of the generator, that is ~ . However, if an object is moving at an accelerated rate, this means that some force is acting on it from another object. In turn, this other object experiences the opposite effect (according to Newton’s 3rd law), and it turns out that m 1 a 1 = − m 2 a 2 . It turns out that two objects emit gravitational waves only in pairs, and as a result of interference they are mutually canceled out almost completely. Therefore, gravitational radiation in the general theory of relativity always has the multipole character of at least quadrupole radiation. In addition, for non-relativistic emitters in the expression for the radiation intensity there is a small parameter where is the gravitational radius of the emitter, r- its characteristic size, T- characteristic period of movement, c- speed of light in vacuum.

The strongest sources of gravitational waves are:

  • colliding (giant masses, very small accelerations),
  • gravitational collapse of a binary system of compact objects (colossal accelerations with a fairly large mass). As a special and most interesting case - merger neutron stars. In such a system, the gravitational-wave luminosity is close to the maximum Planck luminosity possible in nature.

Gravitational waves emitted by a two-body system

Two bodies moving in circular orbits around a common center of mass

Two gravitational bound body with the masses m 1 and m 2, moving non-relativistically ( v << c) in circular orbits around their common center of mass at a distance r from each other, emit gravitational waves of the following energy, on average over the period:

As a result, the system loses energy, which leads to the convergence of bodies, that is, to a decrease in the distance between them. Speed ​​of approach of bodies:

For the Solar System, for example, the greatest gravitational radiation is produced by the and subsystem. The power of this radiation is approximately 5 kilowatts. Thus, the energy lost by the Solar System to gravitational radiation per year is completely negligible compared to the characteristic kinetic energy of bodies.

Gravitational collapse of a binary system

Any double star, when its components rotate around a common center of mass, loses energy (as assumed - due to the emission of gravitational waves) and, in the end, merges together. But for ordinary, non-compact, double stars, this process takes a very long time, much longer than the present age. If a compact binary system consists of a pair of neutron stars, black holes, or a combination of both, then the merger can occur within several million years. First, the objects come closer together, and their period of revolution decreases. Then, at the final stage, a collision and asymmetric gravitational collapse occurs. This process lasts a fraction of a second, and during this time energy is lost into gravitational radiation, which, according to some estimates, amounts to more than 50% of the mass of the system.

Basic exact solutions of Einstein's equations for gravitational waves

Bondi-Pirani-Robinson body waves

These waves are described by a metric of the form . If we introduce a variable and a function, then from the general relativity equations we obtain the equation

Takeno Metric

has the form , -functions satisfy the same equation.

Rosen metric

Where to satisfy

Perez metric

Wherein

Cylindrical Einstein-Rosen waves

In cylindrical coordinates, such waves have the form and are executed

Registration of gravitational waves

Registration of gravitational waves is quite difficult due to the weakness of the latter (small distortion of the metric). The devices for registering them are gravitational wave detectors. Attempts to detect gravitational waves have been made since the late 1960s. Gravitational waves of detectable amplitude are born during the collapse of a binary. Similar events occur in the surrounding area approximately once a decade.

On the other hand, the general theory of relativity predicts the acceleration of the mutual rotation of binary stars due to the loss of energy due to the emission of gravitational waves, and this effect is reliably recorded in several known systems of binary compact objects (in particular, pulsars with compact companions). In 1993, “for the discovery of a new type of pulsar, which provided new opportunities in the study of gravity” to the discoverers of the first double pulsar PSR B1913+16, Russell Hulse and Joseph Taylor Jr. was awarded the Nobel Prize in Physics. The acceleration of rotation observed in this system completely coincides with the predictions of general relativity for the emission of gravitational waves. The same phenomenon was recorded in several other cases: for the pulsars PSR J0737-3039, PSR J0437-4715, SDSS J065133.338+284423.37 (usually abbreviated J0651) and the system of binary RX J0806. For example, the distance between the two components A and B of the first binary star of the two pulsars PSR J0737-3039 decreases by about 2.5 inches (6.35 cm) per day due to energy loss to gravitational waves, and this occurs in agreement with general relativity . All these data are interpreted as indirect confirmation of the existence of gravitational waves.

According to estimates, the strongest and most frequent sources of gravitational waves for gravitational telescopes and antennas are catastrophes associated with the collapse of binary systems in nearby galaxies. It is expected that in the near future several similar events per year will be recorded on improved gravitational detectors, distorting the metric in the vicinity by 10 −21 -10 −23 . The first observations of an optical-metric parametric resonance signal, which makes it possible to detect the effect of gravitational waves from periodic sources such as a close binary on the radiation of cosmic masers, may have been obtained at the radio astronomical observatory of the Russian Academy of Sciences, Pushchino.

Another possibility of detecting the background of gravitational waves filling the Universe is high-precision timing of distant pulsars - analysis of the arrival time of their pulses, which characteristically changes under the influence of gravitational waves passing through the space between the Earth and the pulsar. Estimates for 2013 indicate that timing accuracy needs to be improved by about one order of magnitude to detect background waves from multiple sources in our Universe, a task that could be accomplished before the end of the decade.

According to modern concepts, our Universe is filled with relic gravitational waves that appeared in the first moments after. Their registration will make it possible to obtain information about the processes at the beginning of the birth of the Universe. On March 17, 2014 at 20:00 Moscow time at the Harvard-Smithsonian Center for Astrophysics, an American group of researchers working on the BICEP 2 project announced the detection of non-zero tensor disturbances in the early Universe by the polarization of the cosmic microwave background radiation, which is also the discovery of these relict gravitational waves . However, almost immediately this result was disputed, since, as it turned out, the contribution was not properly taken into account. One of the authors, J. M. Kovats ( Kovac J. M.), admitted that “the participants and science journalists were a bit hasty in interpreting and reporting the data from the BICEP2 experiment.”

Experimental confirmation of the existence

The first recorded gravitational wave signal. On the left is data from the detector in Hanford (H1), on the right - in Livingston (L1). Time is counted from September 14, 2015, 09:50:45 UTC. To visualize the signal, it is filtered with a frequency filter with a passband of 35-350 Hertz to suppress large fluctuations outside the high sensitivity range of the detectors; band-stop filters were also used to suppress the noise of the installations themselves. Top row: voltages h in the detectors. GW150914 first arrived at L1 and 6 9 +0 5 −0 4 ms later to H1; For visual comparison, data from H1 are shown in the L1 plot in reversed and time-shifted form (to account for the relative orientation of the detectors). Second row: voltages h from the gravitational wave signal, passed through the same 35-350 Hz bandpass filter. The solid line is the result of numerical relativity for a system with parameters compatible with those found based on the study of the GW150914 signal, obtained by two independent codes with a resulting match of 99.9. The gray thick lines are the 90% confidence regions of the waveform reconstructed from the detector data by two different methods. The dark gray line models the expected signals from the merger of black holes, the light gray line does not use astrophysical models, but represents the signal as a linear combination of sinusoidal-Gaussian wavelets. The reconstructions overlap by 94%. Third row: Residual errors after extracting the filtered prediction of the numerical relativity signal from the filtered signal of the detectors. Bottom row: A representation of the voltage frequency map, showing the increase in the dominant frequency of the signal over time.

February 11, 2016 by the LIGO and VIRGO collaborations. A merger signal of two black holes with an amplitude at maximum of about 10 −21 was recorded on September 14, 2015 at 9:51 UTC by two LIGO detectors in Hanford and Livingston, 7 milliseconds apart, in the region of maximum signal amplitude (0.2 seconds) combined the signal-to-noise ratio was 24:1. The signal was designated GW150914. The shape of the signal matches the prediction of general relativity for the merger of two black holes with masses of 36 and 29 solar masses; the resulting black hole should have a mass of 62 solar and a rotation parameter a= 0.67. The distance to the source is about 1.3 billion, the energy emitted in tenths of a second in the merger is the equivalent of about 3 solar masses.

Story

The history of the term “gravitational wave” itself, the theoretical and experimental search for these waves, as well as their use for studying phenomena inaccessible to other methods.

  • 1900 - Lorentz suggested that gravity “...can spread at a speed no greater than the speed of light”;
  • 1905 - Poincaré first introduced the term gravitational wave (onde gravifique). Poincaré, on a qualitative level, removed the established objections of Laplace and showed that the corrections associated with gravitational waves to the generally accepted Newtonian laws of gravity of order cancel, thus the assumption of the existence of gravitational waves does not contradict observations;
  • 1916 - Einstein showed that, within the framework of general relativity, a mechanical system will transfer energy to gravitational waves and, roughly speaking, any rotation relative to fixed stars must sooner or later stop, although, of course, under normal conditions, energy losses of the order of magnitude are negligible and practically not measurable (in In this work, he also mistakenly believed that a mechanical system that constantly maintains spherical symmetry can emit gravitational waves);
  • 1918 - Einstein derived a quadrupole formula in which the emission of gravitational waves turns out to be an effect of order , thereby correcting the error in his previous work (an error remained in the coefficient, the wave energy is 2 times less);
  • 1923 - Eddington - questioned the physical reality of gravitational waves "...propagating...at the speed of thought." In 1934, when preparing the Russian translation of his monograph “The Theory of Relativity,” Eddington added several chapters, including chapters with two options for calculating energy losses by a rotating rod, but noted that the methods used for approximate calculations of general relativity, in his opinion, are not applicable to gravitationally bound systems , so doubts remain;
  • 1937 - Einstein, together with Rosen, investigated cylindrical wave solutions to the exact equations of the gravitational field. During the course of these studies, they began to doubt that gravitational waves may be an artifact of approximate solutions of the general relativity equations (correspondence regarding a review of the article “Do gravitational waves exist?” by Einstein and Rosen is known). Later, he found an error in his reasoning; the final version of the article with fundamental changes was published in the Journal of the Franklin Institute;
  • 1957 - Herman Bondi and Richard Feynman proposed the “beaded cane” thought experiment in which they substantiated the existence of physical consequences of gravitational waves in general relativity;
  • 1962 - Vladislav Pustovoit and Mikhail Herzenstein described the principles of using interferometers to detect long-wave gravitational waves;
  • 1964 - Philip Peters and John Matthew theoretically described gravitational waves emitted by binary systems;
  • 1969 - Joseph Weber, founder of gravitational wave astronomy, reports the detection of gravitational waves using a resonant detector - a mechanical gravitational antenna. These reports give rise to a rapid growth of work in this direction, in particular, Rainier Weiss, one of the founders of the LIGO project, began experiments at that time. To date (2015), no one has been able to obtain reliable confirmation of these events;
  • 1978 - Joseph Taylor reported the detection of gravitational radiation in the binary pulsar system PSR B1913+16. Joseph Taylor and Russell Hulse's research earned them the 1993 Nobel Prize in Physics. As of early 2015, three post-Keplerian parameters, including period reduction due to gravitational wave emission, had been measured for at least 8 such systems;
  • 2002 - Sergey Kopeikin and Edward Fomalont used ultra-long-baseline radio wave interferometry to measure the deflection of light in the gravitational field of Jupiter in dynamics, which for a certain class of hypothetical extensions of general relativity makes it possible to estimate the speed of gravity - the difference from the speed of light should not exceed 20% (this interpretation does not generally accepted);
  • 2006 - the international team of Martha Bourgay (Parkes Observatory, Australia) reported significantly more accurate confirmation of general relativity and its correspondence to the magnitude of gravitational wave radiation in the system of two pulsars PSR J0737-3039A/B;
  • 2014 - Astronomers at the Harvard-Smithsonian Center for Astrophysics (BICEP) reported the detection of primordial gravitational waves while measuring fluctuations in the cosmic microwave background radiation. At the moment (2016), the detected fluctuations are considered not to be of relict origin, but are explained by the emission of dust in the Galaxy;
  • 2016 - international LIGO team reported the detection of the gravitational wave transit event GW150914. For the first time, direct observation of interacting massive bodies in ultra-strong gravitational fields with ultra-high relative velocities (< 1,2 × R s , v/c >0.5), which made it possible to verify the correctness of general relativity with an accuracy of several post-Newtonian terms of high orders. The measured dispersion of gravitational waves does not contradict previously made measurements of the dispersion and upper bound on the mass of a hypothetical graviton (< 1,2 × 10 −22 эВ), если он в некотором гипотетическом расширении ОТО будет существовать.


The free surface of a liquid in equilibrium in a gravitational field is flat. If under the influence of any external influence When the surface of a liquid is removed from its equilibrium position in some place, motion occurs in the liquid. This movement will propagate along the entire surface of the liquid in the form of waves, called gravitational waves, since they are caused by the action of the gravitational field. Gravitational waves occur mainly on the surface of the liquid, capturing its internal layers the less, the deeper these layers are located.

We will consider here gravitational waves in which the speed of moving fluid particles is so small that the term in Euler’s equation can be neglected compared to It is easy to find out what this condition means physically. During a period of time on the order of the period of oscillations performed by liquid particles in a wave, these particles travel a distance on the order of the amplitude a of the wave, therefore the speed of their movement is on the order of Speed ​​v changes noticeably over time intervals on the order of magnitude and over distances on the order of magnitude along the direction of propagation of the wave ( - length waves). Therefore, the derivative of speed with respect to time is of the order of magnitude and with respect to coordinates is of the order of Thus, the condition is equivalent to the requirement

that is, the amplitude of oscillations in the wave should be small compared to the wavelength. In § 9 we saw that if the term in the equation of motion can be neglected, then the motion of the fluid is potential. Assuming the fluid is incompressible, we can therefore use equations (10.6) and (10.7). In equation (10.7) we can now neglect the term containing the square of the velocity; putting and introducing a term into the gravity field we get:

(12,2)

We choose the axis, as usual, vertically upward, and as the x, y plane we choose the equilibrium flat surface of the liquid.

We will denote - the coordinate of points on the surface of the liquid by ; is a function of coordinates x, y and time t. In equilibrium, there is a vertical displacement of the liquid surface as it oscillates.

Let a constant pressure act on the surface of the liquid. Then, according to (12.2), we have on the surface

The constant can be eliminated by redefining the potential (by adding to it a quantity independent of the coordinates. Then the condition on the surface of the liquid takes the form

The small amplitude of oscillations in the wave means that the displacement is small. Therefore, we can assume, to the same approximation, that the vertical component of the velocity of movement of surface points coincides with the time derivative of the displacement. But so we have:

Due to the smallness of the oscillations, it is possible in this condition to take the values ​​of the derivatives at instead. Thus, we finally obtain the following system of equations that determine the motion in a gravitational wave:

We will consider waves on the surface of a liquid, considering this surface to be unbounded. We will also assume that the wavelength is small compared to the depth of the liquid; the liquid can then be regarded as infinitely deep. Therefore, we do not write boundary conditions at the side boundaries and at the bottom of the liquid.

Let us consider a gravitational wave propagating along the axis and uniform along the axis; in such a wave all quantities do not depend on the y coordinate. We will look for a solution that is a simple periodic function of time and coordinate x:

where ( is the cyclic frequency (we will talk about it simply as a frequency), k is the wave vector of the wave, is the wavelength. Substituting this expression into the equation, we obtain the equation for the function

Its solution, decaying into the depth of the liquid (i.e. at ):

We must also satisfy the boundary condition (12.5). Substituting (12.5) into it, we find the connection between the frequency b and the wave vector (or, as they say, the wave dispersion law):

The distribution of velocities in a liquid is obtained by differentiating the potential along the coordinates:

We see that the speed decreases exponentially towards the depth of the liquid. In each given point space (i.e., for given x, z), the velocity vector rotates uniformly in the x plane, remaining constant in magnitude.

Let us also determine the trajectory of liquid particles in the wave. Let us temporarily denote by x, z the coordinates of a moving particle of liquid (and not the coordinates of a fixed point in space), and by - the values ​​of x for the equilibrium position of the particle. Then and on the right side of (12.8) can be approximately written instead of , taking advantage of the smallness of the oscillations. Integration over time then gives:

Thus, liquid particles describe circles around points with a radius that decreases exponentially towards the depth of the liquid.

The speed U of wave propagation is equal, as will be shown in § 67. Substituting here we find that the speed of propagation of gravitational waves on an unlimited surface of an infinitely deep liquid is equal to

It increases with increasing wavelength.

Long gravitational waves

Having considered gravitational waves, the length of which is small compared to the depth of the liquid, we now dwell on the opposite limiting case of waves, the length of which is large compared to the depth of the liquid.

Such waves are called long.

Let us first consider the propagation of long waves in the channel. We will consider the length of the channel (directed along the x axis) to be unlimited. The cross section of the channel can have an arbitrary shape and can vary along its length. The cross-sectional area of ​​the liquid in the channel is denoted by The depth and width of the channel are assumed to be small compared to the wavelength.

We will consider here longitudinal long waves in which the liquid moves along the channel. In such waves, the velocity component along the channel length is large compared to the components

Denoting simply v and omitting small terms, we can write the -component of Euler's equation as

a-component - in the form

(we omit terms quadratic in velocity, since the amplitude of the wave is still considered small). From the second equation we have, noting that on the free surface ) should be

Substituting this expression into the first equation, we get:

The second equation for determining two unknowns can be derived using a method similar to deriving the continuity equation. This equation is essentially a continuity equation applied to the case under consideration. Let us consider the volume of liquid enclosed between two cross-sectional planes of the channel located at a distance from each other. In a unit of time, a volume of liquid equal to will enter through one plane and a volume will exit through the other plane. Therefore, the volume of liquid between both planes will change by