Exploring the Interior of a Black Hole: Space-Like Separation Beyond the Horizon

[LarryS]

Forgetting about the singularity for the moment, is the interior of a black hole a space-like region? That is, are any two events that occcur past the black hole horizon space-like separated?

Thanks in advance.

 

[PeterDonis]

are any two events that occcur past the black hole horizon space-like separated?

No. The simplest way to see this is to note that objects can fall into the region beneath the horizon, which means there must be some timelike separated events there (the ones on the worldlines of the infalling objects).

 

[Nugatory]

Forgetting about the singularity for the moment, is the interior of a black hole a space-like region? That is, are any two events that occcur past the black hole horizon space-like separated?

The phrase "spacelike region" makes no sense.
Whether inside or outside the event horizon, everything in the past and future light cones of a given event is timelike-separated from that event, and everything outside those light cones is spacelike separated.

 

[LarryS]

No. The simplest way to see this is to note that objects can fall into the region beneath the horizon, which means there must be some timelike separated events there (the ones on the worldlines of the infalling objects).

I think I see. Are you referring to that section of that worldline that is 100% spatially contained in the black hole?

 

[PeterDonis]

Are you referring to that section of that worldline that is 100% spatially contained in the black hole?

Yes.