Thermodynamics and Luminosities of Rainbow Black Holes

TL;DR

This paper explores how rainbow gravity, a quantum gravity model, affects black hole thermodynamics and luminosities, revealing minimum masses and significant variations in Hawking radiation depending on model parameters.

Contribution

It investigates thermodynamical properties and luminosities of black holes within rainbow gravity, highlighting the impact of modified dispersion relations on black hole behavior.

Findings

Existence of non-zero minimum masses for black holes with certain parameters.

Luminosities of black holes can be greatly suppressed or enhanced.

Rainbow gravity modifies Hawking temperature and event horizon radius.

Abstract

Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. As a result of the nonlinearity of the Lorentz transformation, the energy-momentum dispersion relation is modified. One simple way to import DSR to curved spacetime is \textquotedblleft Gravity's rainbow", where the spacetime background felt by a test particle would depend on its energy. Focusing on the \textquotedblleft Amelino-Camelia dispersion relation" which is $E^{2}=m^{2}+p^{2}\left[ 1-\eta\left( E/m_{p}\right) ^{n}\right] $ with $n>0$, we investigate the thermodynamical properties of a Schwarzschild black hole and a static uncharged black string for all possible values of $\eta$ and $n$ in the framework of rainbow gravity. It shows that there are non-vanishing minimum masses for these two black holes in the cases with $\eta<0$ and $n\geq2$. Considering effects of rainbow gravity on both the Hawking temperature and radius of the event horizon, we use the geometric optics approximation to compute luminosities of a 2D black hole, a Schwarzschild one and a static uncharged black string. It is found that the luminosities can be significantly suppressed or boosted depending on the values of $\eta$ and $n$.