Dual curvature tensors and dynamics of gravitomagnetic matter

TL;DR

This paper introduces dual curvature tensors and antisymmetric field equations to describe the dynamics of gravitomagnetic matter, highlighting its topological nature and dual relationship with gravitoelectric charge.

Contribution

It develops a mathematical framework for gravitomagnetic charge using dual curvature tensors and explores its physical properties and dual relationship with traditional mass.

Findings

Dual curvature tensors characterize gravitomagnetic monopole dynamics.

The metric becomes nonanalytic in the presence of gravitomagnetic matter.

A dual relationship between gravitomagnetic and gravitoelectric theories is established.

Abstract

Gravitomagnetic charge that can also be referred to as the {\it dual mass} or {\it magnetic mass} is the topological charge in gravity theory. A gravitomagnetic monopole at rest can produce a stationary gravitomagnetic field. Due to the topological nature of gravitomagnetic charge, the metric of spacetime where the gravitomagnetic matter is present will be nonanalytic. In this paper both the dual curvature tensors (which can characterize the dynamics of gravitational charge/monopoles) and the antisymmetric gravitational field equation of gravitomagnetic matter are presented. We consider and discuss the mathematical formulation and physical properties of the dual curvature tensors and scalar, antisymmetric source tensors, dual spin connection (including the low-motion weak-field approximation), dual vierbein field as well as dual current densities of gravitomagnetic charge. It is shown that the dynamics of gravitomagnetic charge can be founded within the framework of the above dual quantities. In addition, the dual relationship between the dynamical theories of gravitomagnetic charge (dual mass) and gravitoelectric charge (mass) is also taken into account in the present paper.