Dual Komar Mass, Torsion and Riemann-Cartan Manifolds

TL;DR

This paper introduces a new way to source the dual Komar mass in Riemann-Cartan manifolds by extending Einstein's gravity to include torsion, resulting in a non-vanishing dual mass related to a gravitational-magnetic current.

Contribution

It proposes enlarging the phase space of gravity to allow local sources of dual mass via torsion in Einstein-Cartan theory, overcoming previous limitations.

Findings

Dual Komar mass is non-zero on Riemann-Cartan manifolds.

Dual mass is expressed as a volume integral of a torsion-dependent current.

Enlarged phase space enables local sourcing of dual mass.

Abstract

The dual Komar mass generalizes the concept of the NUT parameter and is akin to the magnetic charge in electrodynamics. In asymptotically flat spacetimes it coincides with the dual supertranslation charge. The dual mass vanishes identically on Riemannian manifolds in General Relativity unless conical singularities corresponding to Misner strings are introduced. In this paper we propose an alternative way to source the dual mass locally. We show that this can be done by enlarging the phase space of the theory to allow for a violation of the algebraic Bianchi identity using local fields. A minimal extension of Einstein's gravity that meets this requirement is known as the Einstein-Cartan theory. Our main result is that on Riemann-Cartan manifolds the dual Komar mass does not vanish and is given by a volume integral over a local 1-form gravitational-magnetic current that is a function of the torsion.