Generally Covariant Conservative Energy-Momentum for Gravitational Anyons

TL;DR

This paper develops a covariant conservation law for energy-momentum in gravitational anyons, showing that energy vanishes for specific solutions and confirming the definition's reasonableness through Einstein gravity limits.

Contribution

It introduces a generally covariant energy-momentum conservation law for gravitational anyons using the displacement transform, a novel approach in this context.

Findings

Energy vanishes for Deser's and Clement's solutions.

Energy-momentum currents have superpotentials and are identically conserved.

The energy definition is validated by Einstein gravity limits.

Abstract

We obtain a generally covariant conservation law of energy-momentum for gravitational anyons by the general displacement transform. The energy-momentum currents have also superpotentials and are therefore identically conserved. It is shown that for Deser's solution and Clement's solution, the energy vanishes. The reasonableness of the definition of energy-momentum may be confirmed by the solution for pure Einstein gravity which is a limit of vanishing Chern-Simons coulping of gravitational anyons.