Accelerated Levi-Civita-Bertotti-Robinson Metric in D-Dimensions

TL;DR

This paper derives a new conformally flat accelerated charge metric in arbitrary dimensions, extending the Levi-Civita-Bertotti-Robinson solution, and demonstrates energy loss of charge due to acceleration across all dimensions.

Contribution

It introduces a novel accelerated charge solution in Einstein-Maxwell theory for any dimension, generalizing known metrics and analyzing energy loss mechanisms.

Findings

Derived a conformally flat accelerated charge metric in D dimensions.

Showed charge loses energy due to acceleration in all dimensions.

Connected the new solution to the Levi-Civita-Bertotti-Robinson metric.

Abstract

A conformally flat accelerated charge metric is found in an arbitrary dimension $D$. It is a solution of the Einstein-Maxwell-null fluid with a cosmological constant in $D \ge 4$ dimensions. When the acceleration is zero our solution reduces to the Levi-Civita-Bertotti-Robinson metric. We show that the charge loses its energy, for all dimensions, due to the acceleration.