Dual Komar Mass, Torsion and Riemann-Cartan Manifolds
arXiv:2010.07887
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.
References in corpus (12)
- The Dynamics of General Relativity
- Duality in linearized gravity
- The Double Copy of Electric-Magnetic Duality
- New dual gravitational charges
- Monopoles for Gravitation and for Higher Spin Fields
- Properties of Dual Supertranslation Charges in Asymptotically Flat Spacetimes
- Dual gravitational charges and soft theorems
- Asymptotic gravitational charges
- Gravitational multi-NUT solitons, Komar masses and charges
- Why not a di-NUT? or Gravitational duality and rotating solutions
- Gravitational Wu-Yang Monopoles
- Conserved currents in the Cartan formulation of general relativity