Proving the Existence of Event Horizon in Homogeneous Spacetimes

[hellfire]

Consider a Schwarzschild spacetime. If the singularity due to the point mass is removed (e.g. with an homogeneous matter distribution), does the event horizon disappear? If yes (I assume this is the case), how can be proven that there exists no event horizon if there is no singularity? May be it is enough to show that in the metric for the interior of stars (with homogeneous mass distribution) there is no change of the timelike coordinate from t to r at any r, as in case of the vacuum Schwarzschild solution for r = 2GM (Schutz p. 290)? I was not able to find an expression for the metric of the interior of stars to check this.

 

[pervect]

There's an analysis of the metric of a star with a constant density rho online

http://www.pma.caltech.edu/Courses/ph136/yr2002/chap25/0225.1.pdf

It's very detailed and long, being a chapter from a textbook, you'll probably have to print out & study it to get very far.

The same results are also in MTW's gravitation. This topic came up late in the thread "The Mass of a Body" that you'll find here on Physics Forum, though I'm not sure if there will be anything useful in that discussion for your question.

I think another poster, DW, once posted some formulas about static stars as well, you might try searching the physics forum for that, too.

As far as the event horizon goes, I think the best test is to consider whether or not light can escape from an object. If there are null geodesics that connect the interior of the star to the exterior, it doesn't have an event horizon. [I haven't double-checked this definition though.]

[add]
I should clarify, there should always be ingoing null geodesics, but if there is a horizon, there won't be outgoing ones.

 

[hellfire]

Thanks, pervect, I will take a look. Your proposal to consider the outgoing geodesics to prove whether an event horizon exists or not seams to be the best one, but I can imagine it may be difficult to do the calculations. What do you think about this possibility:

May be it is enough to show that in the metric for the interior of stars (with homogeneous mass distribution) there is no change of the timelike coordinate from t to r at any r, as in case of the vacuum Schwarzschild solution for r = 2GM (Schutz p. 290)?