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As no information is allowed from inside event horizon, how did we figure out that all matter/energy in a black hole is concentrated at a point like singularity.

Say for example how it was ruled out that all the matter was compacted in half, or a third, or a tenth of the volume that is enclosed by event horizon? Wouldn't space time outside event horizon behave same way whether there was a singularity, or a bigger compact body inside EH? Just curious.

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We don't have any black holes conveniently to hand (the nearest is 3000 light years away) so we've never studied a black hole up close and personal. And, as you say, if we did have a black hole next door we could only study the region outside the event horizon. So black holes are currently theoretical objects - that theory being general relativity.

However we know GR works well where we can test it, and we have no reason to suppose it stops working at an event horizon (not strictly true - see below) so we assume that GR correctly describes a black hole both outside and inside the event horizon.

And what GR tells us is that once any object is inside the event horizon there is no way for that object to resist falling into the singularity, and indeed for all but supermassive black holes that fall takes only a few milliseconds as measured by the falling observer. This is because orbits inside the event horizon would require an orbital velocity faster than light, which of course isn't possible. This is why we believe all the mass in a blak hole is concentrated at the singularity.

But not everyone agrees that GR works at or inside the event horizon. Mostly the objections come from quantum gravity, and the most extreme of them is probably the firewall idea. If this is true the spacetime inside the event horizon may not exist at all in any physically meaningful way.

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  • $\begingroup$ If black holes currently are theoretical objects, how did we estimate the number and mass of them in a galaxy. Some places they even tell mass of a black hole. Recent GW discovery specified two BH of specific mass and the mass of merged BH as well. All that information involving theoretical objects? Doesn't it sound like speculation? Or you meant singularity is theoretical, not BH? $\endgroup$ – kpv Jun 18 '17 at 0:19
  • $\begingroup$ The motivating paradox /firewall topic involves entanglement, which itself has not been scrutinized sufficiently enough to even exist in the currently understood non-local/spooky form. Then why are people so opposed (or at least close minded) to scrutinize non-locality of entanglement. $\endgroup$ – kpv Jun 18 '17 at 0:41
  • $\begingroup$ @kpv: we ought to take this to the chat room if you want to discuss it. In brief, to a theoretician a black hole is a specific spacetime geometry while to a cosmologist a black hole is a dense object that will inevitably evolve into the theoretician's geometry given infinite time. See this question for a related discussion. $\endgroup$ – John Rennie Jun 18 '17 at 4:03
  • $\begingroup$ @kpv: see also this question. $\endgroup$ – John Rennie Jun 18 '17 at 4:05

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