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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 horizon r = 2GM and finite v (the black hole horizon) is different from that with r = 2GM and finite u (the white hole horizon) . The metric in Kruskal–Szekeres coordinates covers all of the extended Schwarzschild spacetime in a single coordinate system. Its chief disadvantage is that in those coordinates the metric depends on both the ...
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]
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]
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. [16] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric. [69]
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 ...
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 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 ...