Abstract
We prove there is a unique vacuum solution in split-signature spacetimes with Kleinian SO(2,1) spherical symmetry. We extend our analysis to accommodate a positive or negative cosmological constant and we prove the Kleinian spherically symmetric solutions to Einstein's equation are locally isomorphic to the split-signature analogs of Schwarzschild-(anti)-de Sitter or Nariai spacetimes. Our analysis provides a Kleinian extension of Birkhoff's theorem to metrics with split signature. Axisymmetric vacuum solutions are also considered, including (2,2) signature formulations of the Kerr and Taub-Newman-Unti-Tamburino metrics.
Original language | English (US) |
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Article number | 044007 |
Journal | Physical Review D |
Volume | 109 |
Issue number | 4 |
DOIs | |
State | Published - Feb 15 2024 |
ASJC Scopus subject areas
- Nuclear and High Energy Physics