Entropy spectrum of charged BTZ black holes in massive gravity's rainbow

TL;DR

This paper demonstrates that the entropy of charged BTZ black holes in massive gravity's rainbow is quantized with equally spaced spectra, revealing new properties and phase transition behaviors influenced by black hole parameters and rainbow functions.

Contribution

It introduces the quantization of black hole entropy in massive gravity's rainbow and explores its effects on thermodynamics and phase transitions, a novel approach in this context.

Findings

Entropy spectrum is equally spaced and depends on black hole parameters.

Quantization leads to divergencies and non-zero entropy at zero horizon radius.

New phase transition points and stability conditions are identified due to quantization.

Abstract

Regarding the significant interests in massive gravity and combining it with gravity's rainbow and also BTZ black holes, we apply the formalism introduced by Jiang and Han in order to investigate the quantization of the entropy of black holes. We show that the entropy of BTZ black holes in massive gravity's rainbow is quantized with equally spaced spectra and it depends on the black holes' properties including massive parameters, electrical charge, the cosmological constant and also rainbow functions. In addition, we show that quantization of the entropy results into the appearance of novel properties for this quantity such as; the existence of divergencies, non-zero entropy in vanishing horizon radius and possibility of tracing out the effects of black holes' properties. Such properties are absent in the non-quantized version of these black holes' entropy. Furthermore, we investigate the effects of quantization on the thermodynamical behavior of the solutions. We confirm that due to quantization, novel phase transitions points are introduced and stable solutions are limited to only dS black holes (AdS and asymptotically flat solutions are unstable).