Entropy and temperature of black holes in a gravity’s rainbow

Abstract

The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. One of these contexts is the gravity's rainbow formalism. We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativity. One is the proposal of Magueijo and Smolin and the other is based on a canonical implementation of doubly special relativity put forward recently by the authors. In these scenarios, we obtain modified expressions for the entropy and temperature of black holes. We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass. For the Magueijo and Smolin proposal, this is only possible for some restricted class of models with bounded energy and unbounded momentum. With the proposal of a canonical implementation, on the other hand, the temperature may vanish for more general theories; in particular, the momentum may also be bounded, with bounded or unbounded energy. This opens new possibilities for the outcome of black hole evaporation in the framework of a gravity's rainbow.

Remnant for all black objects due to gravity's rainbow

“…The modified temperature of Schwarzschild black holes in gravity's rainbow was considered in [1,[17][18][19][20] and it was found to be related to the standard temperature T 0 by…”

Charged Particle’s Tunneling in a Modified Reissner-Nordstrom Black Hole

“…The modified Schwarzschild solution in gravity's rainbow has been given [57]. Further, the thermodynamics [39,40,[62][63][64] and geometry structure [65][66][67] of the modified Schwarzschild black hole have been investigated.…”

Covariant anomaly and Hawking radiation from the modified black hole in the rainbow gravity theory

“…As a specific example, the solution of modified Schwarzschild black holes from gravity's rainbow has been presented in [3]. Some interesting properties of gravity's rainbow were investigated [4][5][6][7], other aspects related to DSR were studied in [8,9].…”