Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity

TL;DR

This paper develops a formalism for conserved currents in gravitational theories with quasi-invariant Lagrangians, applying it to teleparallel gravity to compute black hole energy and angular momentum, highlighting the impact of frame choice.

Contribution

It extends conservation law formalism to quasi-invariant Lagrangians and applies it to teleparallel gravity, providing new methods for calculating conserved quantities.

Findings

Energy and angular momentum of Kerr black hole calculated in teleparallel gravity.

Frame choice significantly affects the conserved quantities.

General formalism applicable to a broad class of gravitational models.

Abstract

Conservation laws in gravitational theories with diffeomorphism and local Lorentz symmetry are studied. Main attention is paid to the construction of conserved currents and charges associated with an arbitrary vector field that generates a diffeomorphism on the spacetime. We further generalize previous results for the case of gravitational models described by quasi-invariant Lagrangians, that is, Lagrangians that change by a total derivative under the action of the local Lorentz group. The general formalism is then applied to the teleparallel models, for which the energy and the angular momentum of a Kerr black hole are calculated. The subsequent analysis of the results obtained demonstrates the importance of the choice of the frame.