Two-body problem in 2+1 spacetime dimensions with a negative cosmological constant: two point particles
Two-body problem in 2+1 spacetime dimensions with a negative cosmological constant: two point particles
We work toward the general solution of the two-body problem in 2+1-dimensional general relativity with a negative cosmological constant. The Bañados-Teitelboim-Zanelli (BTZ) solutions corresponding to black holes, point particles and overspinning particles can be considered either as objects in their own right, or as the exterior solution of compact objects with a given mass M and spin J, such as rotating fluid stars. We compare and contrast the metric approach to the group-theoretical one of characterizing the BTZ solutions as identifications of 2+1-dimensional anti-de Sitter spacetime under an isometry. We then move on to the two-body problem. In this paper, we restrict the two objects to the point particle range |J|-1≤M<-|J|, or their massless equivalents, obtained by an infinite boost. (Both anti-de Sitter space and massless particles have M=-1, J=0). We derive analytic expressions for the total mass Mtot and spin Jtot of the system in terms of the six gauge-invariant parameters of the two-particle system: the rest mass and spin of each object, and the impact parameter and energy of the orbit. Based on work of Holst and Matschull on the case of two massless, nonspinning particles, we conjecture that the black hole formation threshold is Mtot=|Jtot|. The threshold solutions are then extremal black holes. We determine when the global geometry is a black hole, an eternal binary system, or a closed universe.
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Gundlach, Carsten
(2024)
Two-body problem in 2+1 spacetime dimensions with a negative cosmological constant: two point particles.
Physical Review D, 110 (4), [045023].
(doi:10.1103/PhysRevD.110.045023).
Abstract
We work toward the general solution of the two-body problem in 2+1-dimensional general relativity with a negative cosmological constant. The Bañados-Teitelboim-Zanelli (BTZ) solutions corresponding to black holes, point particles and overspinning particles can be considered either as objects in their own right, or as the exterior solution of compact objects with a given mass M and spin J, such as rotating fluid stars. We compare and contrast the metric approach to the group-theoretical one of characterizing the BTZ solutions as identifications of 2+1-dimensional anti-de Sitter spacetime under an isometry. We then move on to the two-body problem. In this paper, we restrict the two objects to the point particle range |J|-1≤M<-|J|, or their massless equivalents, obtained by an infinite boost. (Both anti-de Sitter space and massless particles have M=-1, J=0). We derive analytic expressions for the total mass Mtot and spin Jtot of the system in terms of the six gauge-invariant parameters of the two-particle system: the rest mass and spin of each object, and the impact parameter and energy of the orbit. Based on work of Holst and Matschull on the case of two massless, nonspinning particles, we conjecture that the black hole formation threshold is Mtot=|Jtot|. The threshold solutions are then extremal black holes. We determine when the global geometry is a black hole, an eternal binary system, or a closed universe.
Text
2407.04853v1
- Accepted Manuscript
More information
Accepted/In Press date: 1 August 2024
e-pub ahead of print date: 23 August 2024
Identifiers
Local EPrints ID: 494624
URI: http://eprints.soton.ac.uk/id/eprint/494624
ISSN: 2470-0010
PURE UUID: 200c5a70-1671-428e-aac7-a52f915fa94a
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Date deposited: 11 Oct 2024 16:34
Last modified: 12 Oct 2024 01:45
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