# New considerations on Hilbert action and Einstein equations in anisotropic spaces

## TL;DR

This paper generalizes Einstein's equations to Finsler spaces using variational methods and establishes an analogue of energy-momentum conservation in these anisotropic geometries.

## Contribution

It introduces a variational derivation of Einstein equations in Finsler spaces and identifies a conservation law analogous to energy-momentum conservation.

## Key findings

- Generalized Einstein equations for Finsler spaces derived
- Invariance of Finslerian Hilbert action shown
- Analogue of energy-momentum conservation law established

## Abstract

We find the generalization of Einstein equations to Finsler spaces by variational means and, based on the invariance of the Finslerian Hilbert action to infinitesimal transformations, we find the analogue of the energy- momentum conservation law in these spaces.