Two Kerr Black Holes: Possible or Impossible?

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Discussion Overview

The discussion centers around the feasibility of describing a system of two Kerr black holes within the framework of general relativity. Participants explore theoretical aspects, existing solutions, and the challenges associated with modeling such a system.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the possibility of two Kerr black holes existing together, noting that their course material primarily covers stationary solutions and lacks focus on two-body problems.
  • Another participant suggests that while it may be possible, it has not been extensively explored, highlighting the complexity introduced by the lack of obvious symmetry in a two black hole system.
  • A later reply points to the double Kerr solution as a specific reference that may provide insight into the topic.
  • Additional references are provided, including a mention of Misner's work on two Schwarzschild black holes and a paper discussing the superposition of two Kerr solutions, which reportedly does not allow for an equilibrium state.

Areas of Agreement / Disagreement

Participants express uncertainty about the existence and properties of a system of two Kerr black holes, with no consensus reached on the feasibility or implications of such a configuration.

Contextual Notes

Participants note limitations in their current understanding, particularly regarding the lack of equilibrium states in the solutions discussed and the challenges posed by the symmetry of the black holes.

michael879
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Im trying to describe a system of two kerr black holes and I was wondering if this was even possible? I am currently taking a GR course but I've looked through the textbook and we only seem to deal with stationary solutions to einstein's field question (and no two-body problems).
 
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It may well be possible, but it's not been done to my knowledge. The Kerr metric is a vacuum solution, and all its properties come from the spherical symmetry. The symmetry of 2 BHs is not so obvious or helpful.
 
yea that's what I thought.. damn..
 
It is specific, but you might want to lookup the double Kerr solution.

Stephani in Exact Solutions of Einstein's Field Equations briefly mentions this in chapter 34.4.
 
Last edited:
For two Schwarzschild black holes, the classic solution is due to Misner. A search for "Misner Inital Data" will pull up plenty of recent papers that might give you a derivation.

For Kerr black holes, check the paper here:
http://arxiv.org/abs/gr-qc/9806017
 
michael879 said:
Im trying to describe a system of two kerr black holes and I was wondering if this was even possible? I am currently taking a GR course but I've looked through the textbook and we only seem to deal with stationary solutions to einstein's field question (and no two-body problems).

The exact solution describing two Kerr black holes was presented in D. Kramer, G. Neugebauer, "The superposition of two Kerr solutions", Physics Letters A, 75:4, 259-261 (1980). It does not admit an equilibrium state.
 

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