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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.
The Schwarzschild solution, taken to be valid for all r > 0, is called a Schwarzschild black hole. It is a perfectly valid solution of the Einstein field equations, although (like other black holes) it has rather bizarre properties. For r < r s the Schwarzschild radial coordinate r becomes timelike and the time coordinate t becomes spacelike. [22]
This defines the innermost possible instantaneous orbit, known as the innermost circular orbit, which lies at 1.5 times the Schwarzschild radius (for a Black Hole governed by the Schwarzschild metric). This distance is also known as the photon sphere.
The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916. [14] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric. [70]
The equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole. [2]
Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole. The ingoing coordinates are such that the time coordinate follows the proper time of a free-falling observer who starts from far away at zero velocity, and the spatial ...
The black hole event horizon bordering exterior region I would coincide with a Schwarzschild t-coordinate of + while the white hole event horizon bordering this region would coincide with a Schwarzschild t-coordinate of , reflecting the fact that in Schwarzschild coordinates an infalling particle takes an infinite coordinate time to reach the ...
The Schwarzschild radius r s of a mass m is the radius of the event horizon for a non-rotating uncharged black hole of that mass. It is given by r s = 2 G m c 2 , {\displaystyle r_{\text{s}}={\frac {2Gm}{c^{2}}},} where G is the Newtonian constant of gravitation and c is the speed of light .