# Event Horizon.

1. Feb 19, 2012

### cragar

If I had an infinite slab of mass and it had enough mass to become a black hole, would the event horizon be infinitely far away.
Because the G field would be the same value at any distance away from the slab.

Last edited: Feb 20, 2012
2. Feb 21, 2012

### Bill_K

There is no solution in General Relativity corresponding to the gravitational field of an infinite plane mass.

3. Feb 21, 2012

### cragar

that seems weird it seem like you could have that.

4. Feb 23, 2012

### cragar

Are you saying that in GR that configuration is unstable or not possible. Or they don't have a solution for that symmetry yet.

5. Feb 23, 2012

### bcrowell

Staff Emeritus
There are various candidates for the role of uniform gravitational field in GR. None of them is truly satisfactory. One is the Petrov metric.

6. Feb 26, 2012

### Bill_K

This one? This is the only mention I can find of 'the Petrov metric', Ben. How does it represent (even approximately) a uniform gravitational field?

The Petrov solution is introduced ... in the following theorem: The only vacuum solution of
Einstein’s equations admitting a simply-transitive four-dimensional maximal group of motions is given by
ds2 = dr2 + e−2rdz2 + er(cos√3r(dφ2 − dt2) − 2 sin√3r dφ dt)
The solution ... describes a hyperbolic plane H2 (the (r, z)-plane) with a timelike two-plane (t, z) attached to each point.
...
Bonnor pointed out that the solution can be viewed as a special case of the exterior part
of a Lanczos-van Stockum solution describing an infinite cylinder of rigidly rotating dust.

7. Feb 26, 2012

### bcrowell

Staff Emeritus
Yep, that one. The part about "admitting a simply-transitive four-dimensional maximal group of motions" is the justification for calling it a uniform field. I've given a nontechnical discussion here: http://www.lightandmatter.com/html_books/genrel/ch07/ch07.html#Section7.4 [Broken]

Last edited by a moderator: May 5, 2017
8. Feb 26, 2012

### Passionflower

The Einstein Field Equations act like a constraint, only certain configurations are possible. Within this constraint it is postulated that there are more constraints, e.g. energy conditions.

9. Feb 26, 2012

### bcrowell

Staff Emeritus
Do you mean no static solution that would be stable? No static, stable solution that doesn't violate an energy condition? No such solution that could be formed by gravitational collapse?