# Lorentz violation and Gravitoelectromagnetism: Casimir effect and Stefan-Boltzmann law at Finite temperature

## TL;DR

This paper investigates potential Lorentz symmetry violations in gravitoelectromagnetism at finite temperature by calculating the Casimir effect and Stefan-Boltzmann law within the Standard Model Extension framework, using Thermo Field Dynamics.

## Contribution

It introduces a method to analyze Lorentz violation effects in gravitational phenomena at finite temperature using SME and TFD formalisms, focusing on the Casimir effect and Stefan-Boltzmann law.

## Key findings

- Calculated modifications to the Casimir effect due to Lorentz violation.
- Derived changes in the Stefan-Boltzmann law at finite temperature.
- Provided a framework for testing Lorentz symmetry in gravitational contexts.

## Abstract

The standard model and general relativity are local Lorentz invariants. However it is possible that at Planck scale there may be a breakdown of Lorentz symmetry. Models with Lorentz violation are constructed using Standard Model Extension (SME). Here gravitational sector of the SME is considered to analyze the Lorentz violation in Gravitoelectromagnetism (GEM). Using the energy-momentum tensor, the Stefan-Boltzmann law and Casimir effect are calculated at finite temperature to ascertain the level of local Lorentz violation. Thermo Field Dynamics (TFD) formalism is used to introduce temperature effects.