General relativity


December 6, 2021

For an accessible, non-technical introduction to this topic, see Introduction to General Relativity. General Relativity is a relativistic theory of gravity, that is, it describes the influence of the presence of matter, and more generally of energy, on the movement of the stars, taking into account the principles of special relativity. General relativity encompasses and supplants Isaac Newton's theory of universal gravitation, which is its limit to small speeds (compared to the speed of light) and weak gravitational fields. It is mainly the work of Albert Einstein, who developed it between 1907 and 1915 and is considered to be his major achievement. On November 25, 1915, he submitted his manuscript of the theory of general relativity to the section of mathematics and physics of the Royal Prussian Academy of Sciences, which published it on December 2. The names of Marcel Grossmann and David Hilbert are also associated with it, the first having helped Einstein to familiarize himself with the mathematical tools necessary for the understanding of the theory (differential geometry), the second having taken jointly with Einstein the last stages leading to the finalization of the theory after the latter had presented the general ideas to him during the year 1915. General relativity is based on concepts radically different from those of Newtonian gravitation. It states in particular that gravitation is not a force, but the manifestation of the curvature of space (in fact of space-time), curvature itself produced by the distribution of energy, in the form of mass or kinetic energy, which differs according to the observer's frame of reference. This relativistic theory of gravity predicts effects absent from Newtonian theory but verified, such as the expansion of the Universe, gravitational waves and black holes. It does not make it possible to determine certain constants or certain aspects of the universe (in particular its evolution, whether it is finite or not, etc.): observations are necessary to specify parameters or to make choices between several possibilities left by the theory. None of the many experimental tests carried out could fault it. However, questions remain unanswered: mainly on a theoretical level, how general relativity and quantum physics can be united to produce a complete and coherent theory of quantum gravity; and in terms of astronomical or cosmological observations, how to reconcile certain measurements with theoretical forecasts (dark matter, dark energy).


An analogy allowing a visualization of relativity consists in representing space-time in three dimensions as a stretched sheet deforming under the weight of the objects which one puts there. If the tablecloth is taut and has no body on it, a light ball that is rolled over it passes in a straight line. If we place a heavy ball in the center, the tablecloth is deformed and the light ball no longer goes in a straight line, and can even fall towards the heavy ball giving the illusion that the light ball is attracted by the heavy ball while this attraction is the indirect result of the shape of the "sheet" which applies to masses everywhere in it. This analogy seems to suppose an external source of gravitation (which would give weight to the ball deforming the tablecloth), but we must rather consider that it is the gravitation exerted by the ball itself which deforms the space-time around it. contracting towards it, even by transmitting part of its dynamics to it (speed of movement, rotation on itself). Space-time is not three-dimensional, but four (t

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