Infinite Slab of Mass: Black Hole Effects

[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.

 

[Bill_K]

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

 

[cragar]

that seems weird it seem like you could have that.

 

[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.

 

[bcrowell]

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

 

[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 + e^r(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.

 

[bcrowell]

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?

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

 

[Passionflower]

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

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.

 

[bcrowell]

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

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?

What about this?

Krige, J. D., Maharaj, S. D., & McKenzie, J. F.
The gravitational field of a static infinite sheet of matter
Astrophysics and Space Science 145 (1988) 177.
http://articles.adsabs.harvard.edu/full/1988Ap&SS.145..177K