# Inside a huge sphere, which is being converted to a black hole

Suppose the following scenario:

You reside inside a huge stable spherical star with non-lethal environment at its core. The object is so huge and massive, that its radius is only slightly above its Schwarzschild radius.

Then the sphere is bombarded with high-density energy (sth. like neutron soup) from all sides, increasing the Schwarzschild radius to the point where an event horizon forms. All this would happen at the perimeter of your habitat, without you noticing it.

Are you now trapped inside an event horizon (I think, yes)?

Would your local metric change as soon as you "see" the horizon forming events? Or would it remain the same until the gravitational collapse "gets" you?

Would it in theory be possible to generate enough outward pressure to stop the gravitational collapse, i.e. is the pressure of gravitational collapse finite?

The motivation of this question is the description of spherical objects by an outer Schwarzschild metric and an inner part, which is "stapled", so that it fits and solves Einstein's equations. I always asked myself, whether there was a solution which stapled a non-vacuum metric to the Schwarzschild metric inside the event horizon.

• What do you mean by "stapling" in the inner and outer parts? Are you referring to Kruskal-Szekeres coordinates? Aug 4, 2014 at 17:45
• Seems related. By stapling I mean solving Einstein's equations twice. Once in vacuum, where the solution will be the Schwarzschild metric and once in the region where there is non-zero energy density inside the black hole. And then you need to satisfy boundary conditions between the two parts (i.e. staple them together). Aug 5, 2014 at 10:00
• Ah, I see what you mean. I had meant using Kruskal-Szekeres coordinates to study the Schwartzschild metric under vacuum conditions, i.e. after the black hole formed and assuming zero energy density except at the singularity. I think I interpreted your question wrong, though. You have an interesting point. +1. Aug 5, 2014 at 12:11

There is a completely smooth exact solution to Einstein's equation known as Oppenheimer-Snyder collapse that describes this exact scenario (aside from the star being initially stable). There is no sudden local change in the metric when the event horizon forms. The only way local observers could know is if they try to send a signal to infinity and wait long enough to see it doesn't get there.

This is generic of event horizons, since event horizons are global proeprties of a spacetime that have nothing to do with the local metric. It is in fact possible to be inside an event horizon in a region that is exactly equal to Minkowski space. (Imagine being inside a shell of collapsing matter).

And no, there is no force that can save a matter distribution from collapsing after it has been compressed inside of its Schwarzschild radius.

If I have more time and think of it, I will expand this answer with more details of the collapse, and a penrose diagram of it.

• Reminder: I'd be interested in an elaboration! :)
– Danu
Aug 12, 2014 at 10:56

**In a 'radiation structured' BH, which I've attempted to described in earlier posts, an interior observer would 'disappear' into pure radiation, together with all of the matter that was contained in the proto-BH object. This radiation would, I believe, be manifested at or near the surface of the Schwarzschild envelope. And there would be no singularity involved in this transformation of energy.

Concrete scenarios of “local metric changes during observation of the horizon-forming events” depend on details of the latter (how rapidly, how symmetrically, etc.), but generally your material structures that provide a “non-lethal environment” would fail before you will be able to notice that an event horizon forms. Failure of these shielding structures means that the density becomes high, thence the space becomes curved (so, local metric will change) and will soon develop a singularity.

Also, verifying that you’re below the horizon requires sending a light-speed signal outwards and observing (say, by its echo) whether does it exit your star in a reasonable time. Although the chronometry of your hypothetical sub-Schwarzschildean star facilitates such checks from the core (I assume General Relativity, of course), you will not have time to obtain an answer after the horizon formed.

Yeah, also the stopping-the-collapse question. Some form of it was investigated theoretically, but… you apparently wants something else. Frankly speaking I’m not a GR expert, but no, with an ordinary matter and fields you will not be able to evade the singularity; AFAIK such questions were investigated by Roger Penrose. If exotic matter or fields will be in your possession, then possibly you can create a new universe and save a part of the falling matter from its doom in the singularity, or effect other spacetime changes, but you will not able to break through the horizon into external universe in any case. The old universe will remain in your past forever (again, assuming the plain GR without possibilities to mangle the smooth structure of the spacetime Lorentzian manifold).