Parity-odd and $CPT$-even electrodynamics of the standard model extension at finite temperature

This work examines the finite temperature properties of the $CPT$-even and parity-odd electrodynamics of the standard model extension. The starting point is the partition function computed for an arbitrary and sufficiently small tensor $(k_F{)}_{\alpha \nu \rho \phi }$ [see R. Casana, M. M. Ferreira, Jr., J. S. Rodrigues, and M. R. O. Silva, Phys. Rev. D 80, 085026 (2009).]. After specializing the Lorentz-violating tensor $(k_F{)}_{\alpha \nu \rho \phi }$ for the leading-order-nonbirefringent and parity-odd coefficients, the partition function is explicitly carried out, showing that it is a power of the Maxwell partition function. Also, it is observed that the Lorentz invariance violation coefficients induce an anisotropy in the black-body angular energy density distribution. Planck’s radiation law retains its usual frequency dependence and the Stefan-Boltzmann law keeps the same form, except for a global proportionality constant.