We say that if any particles from outside fall into the black hole, they eventually hit singularity. Then why not particles already inside the black hole are at singularity? Or are they? If yes, then why does a black hole have a finite size?
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All the matter in the black hole exists at the singularity. The singularity is a point of infinite density.
The Schwarzschild black hole is the simplest type of black holes that Einstein's equations predict. These are non-rotating and uncharged. The singularity is enclosed by a boundary called an event horizon. At this boundary, the escape velocity from the black hole becomes equal to the speed of light. Since nothing can exceed speed of light, the event horizon is the boundary from which nothing can get out. When speaking of size of a black hole, people usually mean the radius or diameter of the event horizon. The event horizon is perfectly spherical in a Schwarzschild blackhole. Matter entering such a black hole cannot escape being destroyed by tidal forces and getting infinitely compressed at the singularity.
There are other more complex kind of black holes, which include rotating black holes, charged black holes etc. Though all of them have a singularity and an event horizon (sometimes even multiple event horizons), It is much more difficult to predict what happens to matter in these black holes. For example, in a rotating black hole, It may be possible to avoid the singularity because it exists not at a point, but as a ring. It may be possible to enter new regions of spacetime by passing through a rotating black hole.
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A singularity is a hole, cut, rip or tear in a spacetime manifold. Any geodesics coming to it necessarily end there because the manifold ends there. In the worst case, the curvature resulting from the Schwarzschild solution tips all light cones inside the event horizon towards the singularity. Since all and any time-like geodesics and worldlines are bounded by light (null) cones, they all must end at the singularity, and since you cannot stop moving in time, you will meet your end there inevitably after crossing the event horizon. The singularity is literally your future, no matter what your motion or reference frame, accelerated or inertial since even though those are relative, the bounding light cones are not--they and their tipping into the black hole are invariant for all observers. For this reason, this type of singularity is called spacelike.
Other solutions like rotating or charged black holes (Kerr, Reissner-Nordstrom) don't bend spacetime enough to tip all light cones inward, so a time-like geodesic or worldline need not end at the singularity and instead can keep going indefinitely alongside it even after crossing the event horizon. Thus, this singularity is called timelike.
I hope you guys liked my explanation based on my memory of The Large Scale Structure of Spacetime by Hawking and Elis
