The extension of Schwarzschild line element to include uniformly accelerated mass

TL;DR

This paper extends the Schwarzschild solution to include uniformly accelerated masses, deriving new spacetime line elements and analyzing their properties for potential astrophysical applications.

Contribution

The paper introduces a novel extension of the Schwarzschild metric to uniformly accelerated masses, providing explicit line elements for different acceleration directions.

Findings

Derived the spacetime line element for uniformly moving Schwarzschild objects.

Extended the line element to uniformly accelerated Schwarzschild objects in various directions.

Analyzed the limiting conditions for the new solutions.

Abstract

In this paper we analyze the spacetime geometry due to a Schwarzschild object having uniform accelerated motion. In the beginning, we investigate the gravitational field due to a uniformly moving Schwarzschild object and obtain the spacetime line element for such an object. After analyzing the necessary limiting conditions, the obtained line element is found to be consistent. Next, we extend our work to a uniformly accelerated Schwarzschild object. In that case, we obtain the spacetime line element for both when the acceleration is along the $X-$direction and when the acceleration is in an arbitrary direction on the $XY$ plane (in the later case $X$ may be some third reference direction, which may be useful for future work). The limiting conditions of those line elements have been examined. Such work will have relevant applications in astrophysics when we calculate the geodesic equations of test particles in the gravitational field of objects having uniform accelerated motion.