Reissner-Nordstr\"om and Kerr-like solutions in Finsler-Randers Gravity

TL;DR

This paper extends Finsler-Randers gravity to include charged and rotating solutions, deriving modified field equations and analyzing particle trajectories to identify deviations from general relativity.

Contribution

It introduces Reissner-Nordstr"om and Kerr-like solutions within Finsler-Randers gravity, expanding the framework beyond previous spherically symmetric cases.

Findings

Derived modified gravitational field equations for charged and rotating solutions.

Analyzed geodesic equations showing deviations from general relativity.

Discussed potential observational signatures of Finslerian deviations.

Abstract

In a previous study we investigated the spherically symmetric Schwarzschild and Schwarzschild-de Sitter solutions within a Finsler-Randers-type geometry. In this work we extend our analysis to charged and rotating solutions, focusing on the Reissner-Nordstr\"om and Kerr-like metrics in the Finsler-Randers gravitational framework. In particular, we extract the modified gravitational field equations and we examine the geodesic equations, analyzing particle trajectories and quantifying the deviations from their standard counterparts. Moreover, we compare the results with the predictions of general relativity, and we discuss how potential deviations from Riemannian geometry could be reached observationally.