Infinite Slab of Mass: Black Hole Effects

In summary, the article discusses the impossibility of a static solution for a gravitational field of an infinite plane mass.
  • #1
cragar
2,552
3
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.
 
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  • #2
There is no solution in General Relativity corresponding to the gravitational field of an infinite plane mass.
 
  • #3
that seems weird it seem like you could have that.
 
  • #4
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
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
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
Bill_K said:
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 [Broken]
 
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  • #8
cragar said:
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.
 
  • #9
Bill_K said:
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
 

1. What is an infinite slab of mass in relation to black holes?

An infinite slab of mass refers to a theoretical model used to study the effects of black holes. It assumes an infinite, flat sheet of matter with uniform density and thickness, which can help simplify calculations and predictions about the behavior of black holes.

2. How does an infinite slab of mass affect the formation of black holes?

The infinite slab of mass model helps us understand the gravitational collapse of matter into a black hole. As matter within the slab begins to collapse under its own weight, it becomes increasingly dense and eventually reaches a point where it becomes a black hole.

3. Can an infinite slab of mass exist in reality?

No, an infinite slab of mass is a purely theoretical model used for mathematical calculations and predictions. In reality, matter is not uniformly distributed and there are no perfectly infinite or flat structures.

4. How does the infinite slab of mass model account for the effects of black holes on spacetime?

The infinite slab of mass model is based on Einstein's theory of general relativity, which describes how matter and energy can curve and distort the fabric of spacetime. In this model, the infinite slab of mass creates a strong gravitational field that warps spacetime, leading to the formation of a black hole.

5. What are some limitations of the infinite slab of mass model in studying black holes?

While the infinite slab of mass model can provide valuable insights and predictions, it is a simplified model that does not account for all the complexities of black holes. For example, it does not consider the rotation or charge of black holes, which can have significant effects on their behavior. Additionally, the model assumes a perfectly uniform slab of matter, which may not accurately represent real-world scenarios.

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