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

TL;DR

This paper extends the concept of the Kodama vector and quasilocal mass to three-dimensional axisymmetric spacetimes, including rotating cases with angular momentum, providing tools for analyzing dynamical, non-spherically symmetric spacetimes.

Contribution

The paper introduces a generalized Kodama vector and a quasilocal mass definition that incorporate angular momentum in three-dimensional axisymmetric spacetimes, expanding previous spherically symmetric frameworks.

Findings

Extended Kodama vector to axisymmetric rotating spacetimes

Defined a quasilocal mass including angular momentum

Applicable to dynamical three-dimensional 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.