Transferring Energy in General Relativity

TL;DR

This paper introduces an explicit interaction tensor in general relativity to describe how gravitational fields transfer energy and momentum between distant objects, extending classical ideas to relativistic contexts.

Contribution

It constructs a novel interaction tensor linking free gravity and matter, applicable to specific Petrov types, advancing understanding of energy transfer in general relativity.

Findings

Interaction tensor explicitly constructed for free gravity and matter.

Application to Petrov type D and N spacetimes demonstrates energy transfer mechanisms.

Generalizes Newtonian gravitational induction to relativistic scenarios.

Abstract

A problem in general relativity is, how the gravitational field can transfer energy and momentum between different distant places. The issue is that matter stress tensor is locally conserved, with no explicit interaction with the free gravitational field, which is represented by the Weyl tensor. In this paper we explicitly construct an interaction tensor for free gravity and matter, that depicts the interplay between the energy momentum tensor of free gravity, which is taken to be the symmetric two index square root of Bell-Robinson tensor, and matter. This is examined both in the case of Coulomb-like Petrov type D spacetimes and radiation like Petrov type N spacetimes, where a unique square root exists. The first case generalises the Tweedledum and Tweedledee thought experiment regarding gravitational induction in Newtonian gravity to general relativistic scenarios, and the second gives a proposal for how gravitational radiation can transfer energy and momentum between distant objects separated by a vacuum.