On the Finslerian extension of the Schwarzschild metric

TL;DR

This paper introduces a Finslerian extension of the Schwarzschild metric, which asymptotically approaches a locally anisotropic space-time related to very special relativity, providing a new geometric framework for gravitational fields.

Contribution

The paper presents a novel Finslerian extension of the Schwarzschild metric based on heuristic arguments, connecting it to anisotropic space-time models from deformed relativity theories.

Findings

The extended metric asymptotically approaches Bogoslovsky space-time.

It provides a new geometric perspective on gravitational fields.

The approach links Finsler geometry with deformed special relativity.

Abstract

We provide a Finslerian extension of the Schwarzschild metric based on heuristic arguments. The proposed metric asymptotically approaches not the Minkowski space-time but the Bogoslovsky locally anisotropic space-time which arises naturally as a deformation of very special relativity.