The Relativistic Generalization of the Gravitational Force for Arbitrary Spacetimes

TL;DR

This paper extends a force-based formalism in relativity to arbitrary spacetimes, aiming to offer new insights and potentially a workable definition of mass and energy within the theory.

Contribution

It generalizes a force formalism from static spacetimes to all spacetimes, broadening its applicability in relativistic physics.

Findings

Formalism now applicable to arbitrary spacetimes

Potential for a new definition of mass and energy in relativity

Provides a framework for analyzing gravitational forces in complex spacetimes

Abstract

It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary space-times. It is hoped that this formalism may lead to a workable definition of mass and energy in relativity.