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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.
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In these coordinates, the horizon is the black hole horizon (nothing can come out). The diagram for u-r coordinates is the same diagram turned upside down and with u and v interchanged on the diagram. In that case the horizon is the white hole horizon, which matter and light can come out of, but nothing can go in.
It may be instructive to consider what curves of constant Schwarzschild coordinate would look like when plotted on a Kruskal–Szekeres diagram. It turns out that curves of constant r-coordinate in Schwarzschild coordinates always look like hyperbolas bounded by a pair of event horizons at 45 degrees, while lines of constant t-coordinate in ...
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres.In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric spacetime, which is adapted to these nested round spheres.
where = (,) are coordinates and is the Riemannian metric on the 2 sphere of unit radius. That is, these nested coordinate spheres do in fact represent geometric spheres, but the appearance of b ( r 0 ) r {\displaystyle b(r_{0})\,r} rather than r {\displaystyle r} shows that the radial coordinate do not correspond to area in the same way as for ...
Georges Lemaître was the first to show that this is not a real physical singularity but simply a manifestation of the fact that the static Schwarzschild coordinates cannot be realized with material bodies inside the Schwarzschild radius. Indeed, inside the Schwarzschild radius everything falls towards the centre and it is impossible for a ...
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]