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The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass.
There is no coordinate singularity at the Schwarzschild radius (event horizon). The outgoing ones are simply the time reverse of ingoing coordinates (the time is the proper time along outgoing particles that reach infinity with zero velocity). The solution was proposed independently by Paul Painlevé in 1921 [1] and Allvar Gullstrand [2] in 1922.
Timeline of black hole physics – Timeline of black hole physics; John Michell – geologist who first proposed the idea "dark stars" in 1783 [3] Dark star; Pierre-Simon Laplace – early mathematical theorist (1796) of the idea of black holes [4] [5] Albert Einstein – in 1915, arrived at the theory of general relativity
The Kruskal–Szekeres coordinates also apply to space-time around a spherical object, but in that case do not give a description of space-time inside the radius of the object. Space-time in a region where a star is collapsing into a black hole is approximated by the Kruskal–Szekeres coordinates (or by the Schwarzschild coordinates).
Where is the standard Riemannian metric on the unit radius 2-sphere. That is, these nested coordinate spheres do in fact represent geometric spheres with surface area A = 4 π r 0 2 {\displaystyle A=4\pi r_{0}^{2}}
1923 — George David Birkhoff proves that the Schwarzschild spacetime geometry is the unique spherically symmetric solution of the Einstein vacuum field equations 1931 — Subrahmanyan Chandrasekhar calculates, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (at 1.4 solar masses ...
A black hole cosmology (also called Schwarzschild cosmology or black hole cosmological model) is a cosmological model in which the observable universe is the interior of a black hole. Such models were originally proposed by theoretical physicist Raj Kumar Pathria , [ 1 ] and concurrently by mathematician I. J. Good .
Arthur Eddington commented on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse because "a star of 250 million km radius could not possibly have so high a density as the Sun. Firstly, the force of ...