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

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.