Extension of Kodama vector and quasilocal quantities in three-dimensional axisymmetric spacetimes

Abstract

Spherically symmetric spacetimes admit the so-called Kodama vector, which provides a locally conserved current and a preferred time even for dynamical spacetime without any time translation symmetry. A charge associated with this conserved current leads to a quasilocal mass which agrees with the Misner-Sharp mass. In three dimensions, spherically symmetric spacetimes correspond to axisymmetric ones, while axisymmetry allows spacetimes to be rotating with angular momentum. We extend the notion of the Kodama vector to axisymmetric rotating spacetimes in three dimensions. We also define a quasilocal mass taking into account angular momentum in three-dimensional axisymmetric spacetimes.

5 pages; v2: minor changes, reference added; v3: published in PRD

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Cited by in corpus (8)

• Geometrical origin of the Kodama vector
• Fully constrained, high-resolution shock-capturing, formulation of the Einstein-fluid equations in $2+1$ dimensions
• Kodama-like Vector Fields in Axisymmetric Spacetimes
• Charged rotating BTZ solution revisited: New coordinates and algebraic classifications
• Critical collapse of an axisymmetric ultrarelativistic fluid in $2+1$ dimensions
• Kalb-Ramond field, black holes and black strings in (2 + 1)D
• Extremal rotating BTZ black holes cannot be dressed in (anti-)self-dual Maxwell field
• Dynamical axisymmetric compact objects in General Relativity