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).
Highlights
General relativity (GR) is a successful theory of gravity with certain shortcomings; for example, the accelerated expansion of the universe, massive gravitons, and the ultraviolet (UV) behavior cannot be explained with GR
It is notable that Horava–Lifshitz gravity is based on a deformation of the usual energy–momentum dispersion relation in the UV limit, in which it reduces to the usual energy–momentum dispersion relation in the IR limit
It is notable that such a modification of the usual energy–momentum relation has been obtained in discrete spacetime [17], the spin-network in loop quantum gravity (LQG) [18], spacetime foam [19], ghost condensation [20], and non-commutative geometry [21]
Summary
General relativity (GR) is a successful theory of gravity with certain shortcomings; for example, the accelerated expansion of the universe, massive gravitons, and the ultraviolet (UV) behavior cannot be explained with GR. Charged BTZ black holes with the two generalizations of massive gravity and gravity’s rainbow have been studied [82,83,84]. Kunstatter obtained the area spectrum of higher-dimensional spherical symmetric black holes by considering the adiabatic invariant quantity in the following form [88]: Iadiabatic =. A new method was proposed by Majhi and Vagenas in order to quantize the entropy without using QNM They used the idea of relating an adiabatic invariant quantity to the Hamiltonian of the black hole, and obtained an spaced entropy spectrum with its quantum equal to the one obtained by Bekenstein [90]. We obtain the entropy spectrum of BTZ black holes in massive gravity’s rainbow. We investigate the effects of such quantization on the properties of the black holes
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