Infinite Slab of Mass: Black Hole Effects

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Discussion Overview

The discussion revolves around the theoretical implications of an infinite slab of mass in the context of General Relativity (GR) and its potential to form a black hole. Participants explore the nature of gravitational fields produced by such a configuration and the existence of solutions within GR.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether an infinite slab of mass could have an event horizon that is infinitely far away due to a uniform gravitational field.
  • Another participant asserts that there is no solution in GR for the gravitational field of an infinite plane mass.
  • Some participants express confusion about the implications of this lack of solution, questioning if it indicates instability or simply an absence of a solution for that symmetry.
  • Various candidates for representing a uniform gravitational field in GR are mentioned, including the Petrov metric, though its adequacy is debated.
  • A participant references a specific paper discussing the gravitational field of a static infinite sheet of matter, suggesting that there may be relevant solutions not widely recognized.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence of solutions for an infinite slab of mass in GR. There are competing views regarding the stability and nature of such configurations, with some asserting the absence of solutions and others suggesting potential candidates.

Contextual Notes

Limitations include the lack of clarity on the stability of proposed configurations and the dependence on specific energy conditions within GR. The discussion also highlights the unresolved nature of certain mathematical aspects related to infinite mass distributions.

cragar
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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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There is no solution in General Relativity corresponding to the gravitational field of an infinite plane mass.
 
that seems weird it seem like you could have that.
 
Are you saying that in GR that configuration is unstable or not possible. Or they don't have a solution for that symmetry yet.
 
There are various candidates for the role of uniform gravitational field in GR. None of them is truly satisfactory. One is the Petrov metric.
 
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.
 
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
 
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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.
 
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
 

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