Thermal analysis of photon-like particles in rainbow gravity

TL;DR

This paper investigates the thermodynamic properties of photon-like particles in rainbow gravity using two specific dispersion relations, revealing phase transitions and complex mathematical dependencies in the system.

Contribution

It introduces two particular dispersion relations within rainbow gravity and analyzes their thermodynamic behavior, including numerical bounds and analytical expressions involving special functions.

Findings

Identification of a phase transition in the model.

Numerical bounds for thermodynamic functions are estimated.

Analytical expressions involve special mathematical functions.

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 $\zeta(z)$.