On the Preservation of the Local Properties of Time in General Relativity

TL;DR

This paper proposes a modified theory of gravity that preserves local properties of time, introduces electromagnetic potentials as additional degrees of freedom, and couples gravity with electromagnetism, aiming to resolve paradoxes in relativistic rotating frames.

Contribution

It introduces a new postulate preserving local time properties, leading to a unified framework linking gravity and electromagnetism with additional degrees of freedom.

Findings

Resolves paradoxes in relativistic rotating frames

Identifies electromagnetic potentials with new degrees of freedom

Suggests a coupling between gravitational and electromagnetic fields

Abstract

We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve these paradoxes with a single postulate, namely, the preservation of the local properties of time. This postulate forces the introduction of four additional degrees of freedom into the space-time structure whose transformation properties are defined to preserve the local properties of time under arbitrary four-dimensional coordinate transformations. We identify these additional degrees of freedom with the electromagnetic potentials, which thereby acquire a space-time interpretation. The resulting theory is similar to the traditional Einstein-Maxwell theory, differing primarily in the emergence of a coupling between the gravitational and electromagnetic fields. We show that the proposed reformulation of general relativity provides a rich framework for addressing a number of outstanding problems in contemporary gravitational physics.