# Schwarzschild solution of the modified Einstein field equations

## TL;DR

This paper derives a reformulated Schwarzschild solution within a post-Riemannian Finsler spacetime, showing its relation to Newtonian gravity and analyzing the structure of the interior and horizon solutions.

## Contribution

It introduces a new formulation of the Schwarzschild solution in Finsler spacetime, extending classical results to a modified gravity framework.

## Key findings

- Exterior solution asymptotically matches Newtonian gravity
- Event horizon analysis reproduces standard GR results
- Interior solution contains maximally extensible geodesics

## Abstract

A reformulation of the Schwarzschild solution of the linearised Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the interior solution. It is shown that the exterior solution is asymptotically similar to Newtonian gravity at large distances implying that Newtonian gravity is a low energy approximation of the solution. Application of Eddington-Finklestein coordinates is shown to reproduce the results obtained from standard general relativity at the event horizon. Further application of Kruskal-Szekeres coordinates reveals that the interior solution contains maximally extensible geodesics.