The geometric theory of gravitation presented by Albert Einstein in 1915 is known as general relativity, sometimes referred to as the general theory of relativity and Einstein’s theory of gravity. It serves as the current explanation of gravitation in contemporary physics.
A coherent explanation of gravity as a geometric feature of space and time, or four-dimensional spacetime, is provided by general relativity, which generalizes special relativity and improves Newton’s law of universal gravitation. Specifically, the energy and momentum of any matter and radiation present are intimately correlated with the curvature of spacetime. The Einstein field equations, a set of second-order partial differential equations, define the relation.
One way to think of general relativity’s prediction for the almost flat spacetime geometry around stationary mass distributions is via the lens of Newton’s law of universal gravitation, which defines classical gravity. However, some of general relativity’s predictions go beyond classical physics’ application of Newton’s law of universal gravitation. These predictions include gravitational time dilation, gravitational lensing, gravitational redshift of light, Shapiro time delay, and singularities/black holes.
They also address the passage of time, the geometry of space, motion of bodies in free fall, and the propagation of light. Thus far, every test of general relativity has demonstrated that the theory makes sense. General relativity’s time-dependent solutions have given rise to the contemporary framework and allowed us to discuss the universe’s history.
However, since there isn’t a self-consistent theory of quantum gravity, it’s still difficult to reconcile general relativity with the principles of quantum physics. The unification of gravity with the three non-gravitational forces (strong, weak, and electromagnetic) is still a mystery.
The prediction of black holes—zones in space where time and space are warped to the point where nothing can escape from them—is one of the astrophysical consequences of Einstein’s theory. The ultimate state for big stars is a black hole. Supermassive black holes and stellar black holes are thought to be the sources of microquasars and active galactic nuclei. Additionally, it forecasts gravitational lensing, a process in which light is bent and produces numerous images of the same far-off celestial event.
History of General relativity
Relativism was the basis of Henri Poincaré’s 1905 theory of electron dynamics, which he extended to all forces, including gravity. He proposed that relativity was “something due to our methods of measurement,” in contrast to those who believed that gravity was instantaneous or had an electromagnetic foundation.
He demonstrated gravitational wave propagation at the speed of light in his hypothesis.[3] Not long after, Einstein began to consider how to include gravity in his theory of relativity. In 1907, he started a simple eight-year search for a relativistic theory of gravity using a thought experiment involving an observer in free fall (FFO).
His efforts culminated in November 1915 when he presented the Einstein field equations—the foundation of Einstein’s general theory of relativity—to the Prussian Academy of Science, following many digressions and false starts.[4]
These equations describe the effects of matter and radiation on the geometry of space and time.[5] Riemannian geometry, a kind of non-Euclidean geometry, provided Einstein with the essential mathematical structure to fit his physical theories of gravity, which allowed him to build general relativity.[6] Mathematician Marcel Grossmann made this observation, and Grossmann and Einstein published it in 1913.[7]
The nonlinear Einstein field equations are thought to be challenging to solve. When calculating the theory’s early predictions, Einstein employed approximation techniques. However, the Schwarzschild metric—the first non-trivial accurate solution to the Einstein field equations—was discovered in 1916 by astronomer Karl Schwarzschild. The explanation of the last phases of gravitational collapse and the things we currently refer to as black holes was made possible by this approach.
The Reissner–Nordström solution, which is currently connected to electrically charged black holes, was ultimately developed in the same year as the initial steps toward extending Schwarzschild’s solution to electrically charged objects were made.[8] When Einstein expanded his theory to include the entire universe in 1917, relativistic cosmology was born.
But by 1929, research by Hubble and others had demonstrated that the cosmos is expanding. The expanding cosmic solutions, which do not require a cosmological constant, that Friedmann discovered in 1922 are a good fit for this. Lemaître developed the first Big Bang models, which postulate that our universe originated from a very hot and dense state, using these answers.[10] Later on in his life, Einstein called the cosmological constant his greatest mistake.11]
Among physics theories at the time, general relativity was still somewhat of a mystery. Being consistent with special relativity and explaining various effects not explained by the Newtonian theory, it was obviously superior to Newtonian gravity.
Using no arbitrary parameters (also known as “fudge factors”), Einstein demonstrated in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury. In 1919, an expedition headed by Eddington confirmed general relativity’s prediction for the Sun’s deflection of starlight during the total solar eclipse on May 29, 1919,[13] instantly making Einstein famous.[14]
However, the theory was outside the mainstream of theoretical physics and astrophysics until advancements that took place during what is now described as the “golden age of general relativity,” roughly from 1960 to 1975.[15] As physics gained more understanding of black holes, they recognized quasars as one of their astrophysical byproducts.[16] The theory’s ability to predict outcomes was validated by increasingly accurate testing on the solar system [17], and direct observational tests were also feasible for relativistic cosmology.[18]
The theory of general relativity has gained recognition as an exceptionally elegant concept.[2][19][20] According to Subrahmanyan Chandrasekhar, general relativity demonstrates on a number of levels what Francis Bacon called a “strangeness in the proportion”—that is, features that astonish and amaze people. It contrasts two basic ideas that were previously thought to be totally separate: space and time vs matter and motion.
Chandrasekhar also pointed out that there was a “element of revelation” in the process by which Einstein arrived at his theory, as the principle of equivalency and his belief that a correct description of gravity should have a geometrical foundation served as his only guides in his quest for an exact theory.[21] The simplicity of the general theory of relativity is another aspect of its beauty.
“The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics,” stated Einstein in the preface of Relativity: The Special and the General Theory.
Despite the book’s brief length, the work assumes a level of education equivalent to a university entrance exam as well as a reasonable degree of patience and willpower on the reader’s behalf. The author has gone to great lengths to ensure that the primary concepts are presented in the clearest and most understandable way possible.
From classical mechanics to general relativity
Geometry of Newtonian gravity
The idea that a body’s motion can be explained as a combination of free (or inertial) motion and deviations from this free motion is at the core of classical mechanics. According to Newton’s second rule of motion, which states that the net force acting on a body is equal to that body’s (inertial) mass multiplied by its acceleration, such deviations are generated by external forces acting on a body.[26]
The preferred inertial motions are associated with space and time geometry: in classical mechanics, free-moving objects travel in straight lines at a constant speed. Their courses are known as geodesics in modern terminology, which are straight world lines in curved spacetime.In [27]
On the other hand, it would seem reasonable to assume that inertial motions, if recognized by the observation of actual body motions and after accounting for external forces (such friction or electromagnetic), might be utilized to specify a time coordinate and the geometry of space. However, when gravity enters the picture, things get unclear.
The universality of free fall, also known as the weak equivalency principle or the universal equality of inertial and passive-gravitational mass, is based on Newton’s law of gravity and has been independently verified by experiments like that of Eötvös and its successors (see Eötvös experiment). In free fall, a test body’s trajectory depends only on its position and initial speed, not on any of its material properties.[28]
A more straightforward example of this can be found in Einstein’s elevator experiment, which is depicted in the figure on the right. In this experiment, an observer in an enclosed room cannot determine whether the room is stationary in a gravitational field and the ball is accelerating, or whether they are in free space aboard a rocket that is accelerating at a rate equal to that of the gravitational field versus the ball, which has no acceleration upon release.[29]
Because free fall is universal, motion under the effect of gravity cannot be distinguished from inertial motion in any visible way.
In mathematical terms, this new class of preferred movements is the geodesic motion associated with a particular link that depends on the gravitational potential gradient. It too establishes a geometry of space and time. This architecture retains the standard Euclidean geometry for space. All of spacetime, however, is more intricate.
The outcome of transporting spacetime vectors that can indicate a particle’s velocity (time-like vectors) will vary with the particle’s trajectory, as can be demonstrated using straightforward thought experiments that track the free-fall trajectories of various test particles; mathematically speaking, the Newtonian connection is not integrable. It follows that spacetime is bent from this. As a result, the Newton–Cartan theory provides a geometric description of Newtonian gravity that solely makes use of covariant ideas.
Relativistic generalization
Despite its interesting nature, geometric Newtonian gravity is only a limited application of (special) relativistic mechanics because of its foundation in classical mechanics.[32] In terms of symmetry, physics is Lorentz invariant, as in special relativity, as opposed to Galilei invariant, as in classical mechanics, in cases when gravity can be disregarded.
Translations, rotations, boosts, and reflections are all included in the Poincaré group, which is the defining symmetry of special relativity. When dealing with high-energy phenomena at speeds that are close to the speed of light, the distinctions between the two become crucial.[33]
Additional structures arise with Lorentz symmetry. The collection of light cones (see image) defines them.
The light-cones define a causal structure: for every event A, there exist a set of events (like event B in the image) for which it is theoretically possible for A to influence or be influenced by another event (like event C in the image) via signals or interactions that do not need to travel faster than light.
These sets don’t depend on the observer.[34] The light-cones, at least up to a positive scalar component, can be used to reconstruct the semi-Riemannian metric of the spacetime in conjunction with the world-lines of freely falling particles. This describes a conformal geometry, or conformal structure, mathematically[35].