Thermal analysis of photon-like particles in rainbow gravity

Abstract

This work is devoted to study the thermodynamic behavior of photon--like particles within the \textit{rainbow} gravity formalism. To to do this, we chose two particular ansatzs to accomplish our calculations. First, we consider a dispersion relation which avoids UV divergences, getting a positive effective cosmological constant. We provide \textit{numerical} analysis for the thermodynamic functions of the system and bounds are estimated. Furthermore, a phase transition is also expected for this model. Second, we consider a dispersion relation employed in the context of \textit{Gamma Ray Bursts}. Remarkably, for this latter case, the thermodynamic properties are calculated in an \textit{analytical} manner and they turn out to depend on the harmonic series $H_n$, gamma $\Gamma (z)$, polygamma ${\psi }_n(z)$ and zeta Riemann functions $\zeta (z)$.

22 pages, 7 figures

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