General relativity is Einstein's theory of gravity described in geometric language published in 19 16, which represents the highest level of gravity theory research in modern physics. General relativity contains the classical Newton's law of universal gravitation under the framework of special relativity, which is based on the principle of equivalence. In general relativity, gravity is described as the geometric property (curvature) of space-time; This curvature of space-time is directly related to the energy and momentum tensor of matter and radiation in space-time, and its relationship is Einstein's gravitational field equation (second-order nonlinear partial differential equation group). The predictions obtained from general relativity are quite different from those in classical physics, especially about the passage of time, space geometry, the movement of free falling bodies and the propagation of light, such as time expansion in gravitational field, gravitational redshift of light and gravitational time delay effect. The prediction of general relativity has been verified by all the observations and experiments so far-although general relativity is not the only theory describing gravity today, it is the most concise theory that can be consistent with experimental data. However, there are still some problems that have not been solved. Typical is how to unify the laws of general relativity and quantum physics, so as to establish a complete and self-consistent theory of quantum gravity. Einstein's general theory of relativity has a very important application in astrophysics: it directly deduces that some massive stars will eventually become black holes-some areas in space-time are distorted so that even light cannot escape. There is evidence that stellar mass black holes and supermassive black holes are the direct causes of high-intensity radiation emitted by some celestial bodies, such as active galactic nuclei and micro quasars. The deflection of light in the gravitational field will form a gravitational lens phenomenon, which enables people to observe multiple images of the same celestial body at a far distance. General relativity also predicts the existence of gravitational waves, which has been confirmed by indirect observation, while direct observation is the goal of gravitational wave observation programs like LIGO in the world today. In addition, general relativity is the theoretical basis of modern cosmology.

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Relativity is one of the theoretical foundations of modern physics. Discuss the theory of the relationship between material movement and time and space. Founded by Einstein in the early 20th century, and developed with other physicists, the special theory of relativity was founded in 1905, and the general theory of relativity was completed in 19 16. At the end of 19, due to the perfection of Newtonian mechanics and Maxwell's electromagnetic theory (183 1~ 1879), some physicists thought that "the development of physics has actually ended", but when people used galilean transformation to explain the propagation of light and other issues, they found a series of sharp contradictions and put forward the classical view of time and space. Einstein put forward a new concept of time and space in physics, established the law of high-speed moving objects equivalent to the speed of light, and founded the theory of relativity. Special relativity puts forward two basic principles. (1) The principle of light speed invariance. That is to say, in any inertial system, the speed of light C in vacuum is the same, regardless of the movement of the light source and the observer. (2) The principle of special relativity is the basic law of physics, even the natural law, which is the same for all inertial reference systems. Theory of relativity

Einstein's Second Theory of Relativity (19 16). This theory holds that gravity is caused by the distortion of space-time geometry (that is, the geometry that not only considers the distance between points in space, but also considers the distance between points in space and time), so the gravitational field affects the measurement of time and distance. General relativity: Einstein's theory based on the view that the speed of light must be the same for all observers, no matter how they move. It explains the special relativity of gravity and the law of universal gravitation according to the curvature of four-dimensional space-time. Special relativity is the case that there is no gravity; The law of universal gravitation is the situation that the distance is close, the gravity is small and the speed is slow. From a distance of 600 kilometers, we can see the simulation diagram of a black hole whose mass is ten times that of the sun.

With the Milky Way as the background, watch a black hole with ten times the mass of the sun at a distance of 600 kilometers (simulation map).

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1905, Einstein published a paper on the influence of gravity and acceleration on light in special relativity, and the prototype of general relativity began to take shape. 19 12 years, Einstein published another paper to discuss how to describe gravity field in geometric language. At this point, the kinematics of general relativity appeared. 19 15 years, Einstein's field equation was published, and the dynamics of the whole general theory of relativity was finally completed. After 19 15, the development of general relativity mostly focused on solving the field equation, and the physical explanation of the solution and the search for possible experiments and observations also accounted for a large part. However, because the field equation is a nonlinear partial differential equation, it is difficult to solve, so only a few solutions were solved before the computer was applied to science. There are three most famous solutions: Schwarzschild solution (19 16), Reissner-Nordstr? M solution and Kerr solution. The observation of general relativity has also made a lot of progress. The precession of mercury is the first evidence to prove the correctness of general relativity. It was measured before the appearance of relativity, and it was not explained theoretically until Einstein discovered it. In the second experiment, 19 19 Eddington measured the starlight deflection caused by the solar gravitational field during the solar eclipse in Africa, which was completely consistent with the prediction of general relativity. At this time, the general theory of relativity has been widely accepted by the public and most physicists. After that, there were many experiments to test the theory of general relativity and confirm its correctness. In addition, the expansion of the universe has also created another climax of general relativity. Title page of Einstein's manuscript explaining general relativity from 19

Since 22 years, researchers have found that the solution from the field equation will be an expanding universe. Einstein naturally did not believe that the universe would expand or contract at that time, so he added a cosmological constant to the field equation, which made it possible to solve a stable universe. But there are two problems with this solution. Theoretically, the solution of a stable universe is mathematically unstable. In addition, in 1929, Hubble discovered that the universe is actually expanding. This experimental result made Einstein give up the cosmological constant and declared that it was the biggest mistake in my career. But according to the recent observation of a supernova, the expansion of the universe is accelerating. So the cosmological constant seems to have the possibility of resurrection, and the dark energy in the universe may be explained by the cosmological constant.

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To put it simply, the two basic principles of general relativity are: first, the equivalence principle: gravity and inertia force are equivalent; Second, the principle of general relativity: the principle of equivalence

In any reference system, all physical laws adopt the same form.

Equivalence principle

Principle of reciprocity: it can be divided into weak principle and strong principle. The weak equivalence principle holds that gravitational mass and inertial mass are equivalent. According to the principle of strong equivalence, two spaces are subjected to gravity and equal inertial force respectively, and all experiments in these two spaces will get the same physical laws. At present, many scholars are engaged in the demonstration and research of the equivalence principle, but at least as far as the accuracy can be achieved at present, the equivalence principle has not been proved by experiments.

Generalized relativity principle

Principle of general relativity: the form of physical laws is constant in all reference systems. In general physics (college textbooks), these two principles are described as follows: equivalence principle: in an inertial system, all physical phenomena under the action of a uniform and constant gravitational field can be exactly the same as those in a non-inertial system that is not affected by the gravitational field but moves at a constant acceleration. Relativity principle of general relativity: all non-inertial systems and inertial systems existing in the gravitational field are equivalent, which are used to describe physical phenomena.

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General relativity is based on special relativity. If the latter is proved wrong, then the whole theoretical building will collapse.

Two different expressions of quality

In order to understand general relativity, we must know how mass is defined in classical mechanics. First of all, let's think about what quality stands for in our daily life. "Weight"? In fact, we think that mass is something that can be weighed, just like we measure it: we put the object that needs to be measured on the balance. What kind of quality do we use to do this? It is the fact that the earth and the measured object attract each other. This mass is called "the ball falls to the acceleration floor and falls to the earth."

Gravitational mass ". We call it "gravity" because it determines the motion of all stars in the universe: the gravitational mass between the earth and the sun drives the earth to move around the latter in a nearly circular motion. Now, try to push your car on a flat ground. You can't deny that your car strongly resists the acceleration you want to give it. This is because your car is of great quality. It is easier to move light objects than heavy ones. Mass can also be defined in another way: "It opposes acceleration". This mass is called "inertial mass". So we come to the conclusion that we can measure quality in two ways. Either we weigh it (very simply) or we measure its resistance to acceleration (using Newton's law). Many experiments have been done to measure the inertial mass and gravitational mass of the same object. All experimental results come to the same conclusion: inertial mass is equal to gravitational mass. Newton himself realized that this kind of mass equivalence was caused by some reason that his theory could not explain. But he thinks this result is a simple coincidence. On the contrary, Einstein found that there is a channel in this equation that can replace Newton's theory. Everyday experience proves this equivalence: two objects (one light and one heavy) will "fall" at the same speed. However, heavy objects are subject to greater gravity than light objects. So why didn't it "fall" faster? Because it is more resistant to acceleration. The conclusion is that the acceleration of an object in the gravitational field has nothing to do with its mass. Galileo was the first person to notice this phenomenon. It is important for you to understand that all objects in the gravitational field "fall at the same acceleration" is the equivalent result of inertial mass and gravitational mass (in classical mechanics). Now let's pay attention to the expression "whereabouts". Objects "fall" because the gravitational mass of the earth produces the gravitational field of the earth. Two objects have the same acceleration in the same gravitational field. Whether it's the moon or the sun, the light cone

They accelerate at the same speed. In other words, their speed increases by the same amount every second. (Acceleration is the increment of speed per second)

Gravitational mass and inertial mass are equal.

Einstein has been looking for the explanation that "gravitational mass equals inertial mass". To this end, he put forward a third hypothesis, called "equivalence principle". It shows that if an inertial system is uniformly accelerated relative to a Galileo system, then we can consider it (inertial system) to be stationary by introducing a uniformly accelerated gravitational field relative to it. Let's examine an inertial system K', which has a uniform acceleration motion relative to Galileo system. There are many objects around k and k'. This object is stationary with respect to K, so these objects have the same accelerated motion with respect to K'. This acceleration is the same for all objects, contrary to the acceleration direction of K' relative to K. As we have said, the acceleration of all objects in a gravitational field is the same, so the effect is equivalent to that K' is static and has a uniform gravitational field. Therefore, if the equivalence principle is established, it is only a simple inference that two masses of an object are equal. This is why (quality) equivalence is an important argument to support the principle of equivalence. Assuming that K' is static and the gravitational field exists, we can understand K' as a Galileo system, in which we can study the laws of mechanics. Therefore, Einstein established his fourth principle.

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Einstein put forward the "equivalence principle", that is, gravity and inertia force are equivalent. This principle is based on the equivalence of gravitational mass and inertial mass. According to the principle of equivalence, Einstein extended the principle of relativity in a narrow sense to the principle of relativity in a broad sense, that is, the form of physical laws is unchanged in all reference systems. The motion equation of an object is the geodesic equation in the reference system. Geodesic equation has nothing to do with the inherent properties of the object itself, but only depends on the local geometric properties of time and space. And gravity is the expression of local geometric properties of time and space. The existence of material mass will cause the bending of time and space. In curved space-time, objects still move along the shortest distance (that is, along the geodesic-in Euclidean space). For example, the geodesic movement of the earth in curved space-time caused by the sun actually revolves around the sun, resulting in a gravitational effect. Just like on the surface of the earth, if you move in a straight line, you actually walk around the great circle on the surface of the earth. Gravity is the expression of local geometric properties of time and space. Although the general theory of relativity was founded by Einstein, its mathematical basis can be traced back to the axiom of Euclid geometry and the efforts made for centuries to prove Euclid's fifth postulate (that is, parallel lines are always equidistant). This effort culminated in the work of Lobachevsky, Bolyai and Gauss, who pointed out that Euclid's fifth postulate could not be proved by the first four postulates. Gauss's student Riemann developed the general mathematical theory of non-Euclidean geometry. So it is also called Riemannian geometry or surface geometry. Before Einstein developed the general theory of relativity, people thought that non-Euclidean geometry could not be applied to the real world, and the frequency of light waves emitted from the surface of massive objects was red-shifted.

From China. In the general theory of relativity, the role of gravity is "geometric"-that is, the spatial background of Min and the physical picture of universal gravitation in the special theory of relativity have become the physical picture of free movement without external force (assuming no electromagnetic interaction) in the Riemannian spatial background. Its dynamic equation has nothing to do with its own mass and becomes geodesic equation. The law of universal gravitation is changed into Einstein's field equation: r _ UV-1/2 * r * g _ UV = κ * t _ UV (rμ ν-(1/2) gμ ν r = 8g π t μ ν. It is famous for its complexity and beauty, but it is not perfect, and only approximate solutions can be obtained in calculation. Finally, people get the exact solution of true spherical symmetry-Schwartz solution. The field equation after adding the cosmological constant is: r _ uv-1/2 * r * g _ uv+λ * g _ uv = κ * t _ uv.

The application of cosmic phenomena and scientific research in editing this paragraph.

According to general relativity, there is no gravity in the local inertial system, and one-dimensional time and three-dimensional space form a four-dimensional flat Euclidean space. In any frame of reference, there is gravity, which leads to the curvature of space-time, so space-time is a four-dimensional curved non-Euclidean space. Einstein discovered the gravitational field equation that the distribution of matter affects the space-time geometry. The bending structure of time space depends on the distribution of material energy density and momentum density in time space, and the bending structure of time space determines the motion trajectory of objects. When gravity is weak and curvature of spacetime is small, the predictions of general relativity tend to be consistent with those of Newton's law of universal gravitation and Newton's law of motion. But there is a difference between strong gravity and large curvature of spacetime. Since the general theory of relativity was put forward, the abnormal precession of Mercury's perihelion, gravitational redshift of light frequency, gravitational deflection of light and delay of radar echo have been predicted, which have been confirmed by astronomical observations or experiments. In recent years, when the light from the light source passes through the dense star, the observation of the pulse binary star is also deflected.

It provides strong evidence for general relativity to predict the existence of gravitational waves. The general theory of relativity is quickly recognized and appreciated by people because of its amazing confirmation and theoretical beauty. However, because Newton's gravity theory is accurate enough for most gravity phenomena, general relativity only provides a very small correction, which people do not need in practice. Therefore, the general theory of relativity has not been fully valued and developed rapidly in the half century after its establishment. In the 1960s, the situation changed, and the background radiation of strong gravitational celestial bodies (neutron stars) and the 3K universe was discovered, which made the research of general relativity flourish. General relativity is of great significance for studying the structure and evolution of celestial bodies and the structure and evolution of the universe. The formation and structure of neutron stars, black hole physics and black hole detection, gravitational radiation theory and gravitational wave detection, big bang cosmology, quantum gravity and topological structure of large-scale spacetime are being deeply studied, and general relativity has become an important theoretical basis for physical research.

Edit this experimental test of general relativity.

At the beginning of the establishment of general relativity, Einstein put forward three experimental tests, one is the precession of Mercury's perihelion, the other is the bending of light in the gravitational field, and the third is the gravitational red shift of spectral lines. Among them, only the precession of Mercury's perihelion is a definite fact, and the other two items were determined later. After 1960s, some people put forward plans to observe radar echo delay and gravitational waves.

Mercury perihelion precession

1859, astronomer le Villier found that the observed precession of Mercury's perihelion is 38 seconds faster than the theoretical value calculated every hundred years according to Newton's law. He speculated that there might be an asteroid inside Mercury, and the attraction of this asteroid to Mercury led to the deviation between the two. But after years of searching, this asteroid has never been found. 1882, after recalculation, S.Newcomb found that the excess annual difference of Mercury's perihelion was 43 seconds every hundred years. He suggested that the movement of Mercury may be inhibited by diffuse matter emitted by zodiacal light. But this does not explain why several other static particles suspended in space are arranged in a ring.

Planets have similar excess precession. Newcomb wants to know whether gravity obeys inverse square law. Later, some people used electromagnetic theory to explain the abnormal phenomenon of mercury perihelion precession, but none of them succeeded. 19 15 years, Einstein regarded the motion of the planet around the sun as its motion in the gravitational field of the sun according to the general theory of relativity. Due to the curvature of the surrounding space caused by the mass of the sun, the perihelion precession of the planet is ε=24π2a2/T2c2( 1-e2), where A is the long semi-axis of the planet's orbit and C is the speed of light in centimeters. For mercury, ε=43″/ century is calculated, which coincides with Newcomb's result, and solves the unsolved problem of Newton's gravity theory for many years. This result became the most powerful evidence of general relativity at that time. Mercury is the closest inner planet to the sun. The closer to the central celestial body, the stronger the gravitational field and the greater the curvature of space-time bending. In addition, the orbit eccentricity of Mercury is large, so the precession correction value is larger than that of other planets. The excess precession of Venus, Earth and Icarus measured later is basically consistent with the theoretical calculation.

Bending of light in gravitational field

In 19 1 1, Einstein discussed that when light passes near the sun, it will bend under the action of the sun's gravity. He calculated that the deflection angle was 0.83 ",and pointed out that this phenomenon could be observed in the total solar eclipse. 19 14 German astronomer E.F.Freundlich led a team to Klimu Peninsula to observe the total solar eclipse in August of that year, when World War I broke out and the observation failed. Fortunately, because Einstein only considered the equivalence principle at that time, the calculation result was half smaller. 19 16 Einstein recalculated the bending of light in the gravitational field according to the complete general relativity. He not only considered the gravity of the sun, but also considered the spatial geometric deformation caused by the mass of the sun. The deflection angle of light is α =1".75R0/r, where r0 is the radius of the sun and r is the distance from the light to the center of the sun. During the total solar eclipse of 19 19, the Royal Society and the Royal Astronomical Society sent two observation teams led by A.S. Feddington and others to principe island in the Gulf of Guinea in West Africa and Sobral in Brazil for observation. After comparison, the observation results of the two places are 1 ". 6 1 ".30 and1". 980 ".They are 12 respectively. Comparing the deflection angle data measured at that time with Einstein's theoretical expectation, it is basically consistent. This kind of observation accuracy is too low, and it will be interfered by other factors. People have been looking for possibilities other than total solar eclipse. The development of radio astronomy in the 1960s brought hope. A radio source similar to a star was discovered with a radio telescope. The results of observing quasars at 1974 and 1975 show that the deviation between the theoretical values and the observed values is less than 1%.

Gravitational redshift of spectral lines

General relativity points out that the clock runs slowly in a strong gravitational field, so the light emitted from the surface of a massive star to the earth will move to the red end of the spectrum. Einstein discussed this problem in the article 19 1 year. He expressed the gravitational potential difference between the surface of the sun and the earth by φ, and ν0 and ν respectively expressed the frequency of light on the surface of the sun and when it reached the earth, and obtained: (ν 0-ν)/ν =-φ/C2 = 2× 10-6. Einstein pointed out that this result is similar to that of C. Fabry (C.

Test, and fabry thought it was the influence of other reasons. 1925, W.S. Adams of Mount Wilson Observatory observed Sirius A, the companion of Sirius. This companion star is a so-called white dwarf star, which is 2000 times denser than platinum. By observing its spectral lines, the frequency shift obtained is basically consistent with the expectation of general relativity. 1958, Mossbauer effect was discovered. By using this effect, high-resolution R-ray vibration absorption can be measured. 1959, Pound (R.V.Pound) and Rybka (G.Rebka) first proposed a scheme to detect gravitational frequency shift by using Mossbauer effect. Then, they successfully carried out the experiment, and the difference between the results and the theoretical values was about 5%. Good results can also be obtained by measuring gravitational frequency shift with atomic clock. In 197 1, J.C. Havler and R.E. Keating used several cesium atomic clocks to compare the timing rates at different heights. One of them was placed on the ground as a reference clock, and the others were carried into space by civil aviation planes, flying around the earth along the equator at an altitude of 65438+100000 meters. The experimental results are consistent with the theoretical expected values in the range of 65438 00%. 1980, R.F.C viso et al. did experiments with hydrogen maser. They launched the hydrogen maser rocket into the space of 10000 km, and the difference between the results obtained and the theoretical value was only 7× 10-5.

Radar echo delay

The bending phenomenon of light passing near a massive object can be regarded as a kind of refraction, which is equivalent to slowing down the speed of light. Therefore, if the signal from a certain point in space passes near the sun, the time to reach the earth will be delayed. In 1964, I.I.Shapiro first put forward this proposal. His team conducted radar experiments on Mercury, Venus and Mars successively, which proved that the radar echo did have a delay. In recent years, the experimental accuracy has been improved by taking artificial celestial bodies as reflection targets. Compared with the theoretical value of general relativity, the difference between the results of such experiments is about 65438 0%. There are many examples of testing general relativity with astronomical observations. For example: gravitational wave observation and binary star observation, Hubble's law on the expansion of the universe, the discovery of black holes, the discovery of neutron stars, the discovery of microwave background radiation and so on. Through various experiments, the general theory of relativity is more and more convincing. But there is one thing to emphasize: we can deny a theory with one experiment, but we can't prove a theory with a limited number of experiments; An experiment with low accuracy may overturn a theory, but a series of experiments with high accuracy cannot finally confirm a theory. Whether the general theory of relativity is correct or not, people must take a very cautious attitude and draw reasonable conclusions strictly and cautiously.

Edit Einstein's fourth hypothesis in this paragraph

Einstein's fourth hypothesis is a generalization of his first hypothesis. It can be said that the laws of nature are the same in all departments. It is undeniable that it sounds more "natural" to claim that the laws of nature are the same in all departments than to claim that the laws of nature are the same only in Galileo. But we don't know whether there is a Galileo system. This principle is called the principle of general relativity. Death elevator lets us imagine an elevator falling freely in a skyscraper with a fool inside. The man left his watch and handkerchief at the same time. What will happen? For a person who takes the earth as the reference frame outside the elevator, the images of the four same celestial bodies, such as watches, handkerchiefs and people, are all under the gravitational lens effect.

The elevator descends at exactly the same speed. Let's review: according to the principle of equality, the motion of an object in the gravitational field does not depend on its mass. ) So the distance between watch and floor, handkerchief and floor, man and watch, man and handkerchief is fixed. So for the person in the elevator, the watch and handkerchief will be left where he just threw them. If this person gives his watch or handkerchief a certain speed, they will move in a straight line at a constant speed. The elevator behaves like Galileo system. However, this will not last forever. Sooner or later, the elevator will collapse, and the observers outside the elevator will go to an unexpected funeral. Now do the second idealized experiment: our elevator is far away from any mass object. Like the depths of the universe. Our big fool escaped from the last accident. After staying in the hospital for several years, he decided to return to the elevator. Suddenly a creature began to drag the elevator. Classical mechanics tells us that constant force will produce constant acceleration. This rule does not apply to very high speed situations. Because the mass of an object increases with the increase of speed. In our experiment, we assume that it is correct. Therefore, the elevator will accelerate in Galileo. Our genius fool stayed in the elevator and let his handkerchief and watch fall. People in Galileo's department outside the elevator thought that watches and handkerchiefs would hit the floor. This is because the floor hits them (handkerchiefs and watches) because of its acceleration. In fact, people outside the elevator will find that the distance between the watch and the floor and the distance between the handkerchief and the floor are decreasing at the same speed. On the other hand, the person in the elevator will notice that his watch and handkerchief have the same acceleration, which he will attribute to the gravitational field. These two explanations seem to be the same: on the one hand, accelerated motion, on the other hand, consistent motion and gravitational field. Let's do another experiment to prove the existence of gravitational field. A beam of light shone through the window on the opposite wall. Our two observers explained it this way: people outside the elevator told us that light passes through the window at a constant speed (of course! ) shoots horizontally into the elevator along a straight line and shines on the opposite wall. But because the elevator is running upwards, the irradiation point of light should be slightly lower than this incident point. The people in the elevator said, we are in the gravity field. Because light has no mass, it will not be affected by the gravitational field, and it will just fall on the point opposite the incident point. Oh! The problem has arisen. Two observers disagree. However, the people in the elevator made a mistake. He said that light has no mass, but it has energy, and energy has mass (remember that the mass of one joule of energy is: m = e/c 2), so light will have a trajectory that bends to the floor, just as external observers say. Because the mass of energy is very small (C 2 = 300,000,000× 300,000,000), this phenomenon can only be observed near a very strong gravitational field. It has been proved that light will bend when it is close to the sun because of its great mass. This experiment is the first demonstration of Einstein's theory (general relativity). From all these experiments, we draw the conclusion that by introducing the gravitational field, we can regard an acceleration system as a Galileo system. By extension, we think it is suitable for all motions, whether it is rotating motion (centripetal force is interpreted as gravitational field) or non-uniform acceleration motion (gravitational field that does not meet Riemann condition is transformed by mathematical method). You see, general relativity conforms to practice everywhere. The above example is taken from The Evolution of Constitution by Einstein and leopold infeld.

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gravitational lens

Einstein Cross: The deflection effect of light in four imaging gravitational fields of the same celestial body under the gravitational lens effect is the cause of a new astronomical phenomenon. When there is still a massive celestial body between the observer and the distant celestial body, when the mass and relative distance of the celestial body are appropriate, the observer will see multiple distorted celestial bodies imaging, and this effect is called gravitational lens. Influenced by the structure, size and mass distribution of the system, imaging can be repeated, even forming a ring called Einstein ring or a part of the arc of the ring. The earliest gravitational lens effect was discovered in 1979, and more than 100 gravitational lenses have been discovered so far. Even if these images are too close to distinguish-this situation is called gravitational microlens-this effect can still be measured by observing the change of total light intensity, and many gravitational microlenses have been found. Gravitational lens has developed into an important tool for observing astronomy. It has been used to detect the existence and distribution of dark matter in the universe, become a natural telescope to observe distant galaxies, and can also estimate Hubble constant independently. The statistical results of gravitational lens observation data are also of great significance to the study of galaxy structure evolution.

Gravitational wave astronomy