PAllen
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friend said:As I understand it, the time dimension inside a black hole is alway pointed directly to the singularity. So objects that fall inside a BH can only travel with some component of their velocity pointing towards the center. In other words, you can non travel in any direction with a component pointing outwards, you must always have some component inward. I think this means that no object can travel tangentially to the center. So you will ever see objects coming from the side, only from the rear.
Some of this is just peculiarities of the way Schwarzschild coordinates label things. Geometrically, you can say that all forward going timelike curves reach the singularity (in more complex black holes than the spherically symmetric, this is not necessarily true - some can escape to other 'sheets' of the manifold). It is true that you cannot have a time like path remaining on a 2-sphere of constant area around the singularity [ take this a definition of pure tangential motion]. However, you can have tangential components, such that infallers can collide before reaching the singularity.
As for seeing, if you have luminous dust falling in from all radial directions, an ifnaller will see light from all spatial directions until they reach the singularity. What is unusual is that light seen from toward the singularity was actually emitted from a dust particle as of when it was further from the singularity than you are now. You receive it from the direction of the singularity because you 'bump' into the light as it slowly moves inwards, though emitted in an outward direction. Despite this, all looks normal (sufficiently locally). A key point to keep in mind: no matter how extreme the near singular region, a sufficiently small chunk of spacetime behaves just like Minkowski spacetime - this is part of the fundamental definition of a pseudo-riemannian manifold.
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