^{3}.

The emergence of the quantum gravitational effects in a very high energy regime necessitates some corrections to the thermodynamics of black holes. In this letter, we investigate a possible modification to the thermodynamics of Schwarzschild anti-de Sitter (SAdS) black holes due to rainbow gravity model. Using the correspondence between a (

Based on the great discovery of black hole Hawking radiation, it seems that there is a deep connection between three seemingly different branches of science: thermodynamics, gravity, and quantum mechanics in the black holes. In fact, Hawking radiation opens an important window to quantum gravity. Most of the promising candidates for quantum gravity expect the existence of a minimal observable length at the order of the Planck length [

On the other hand, one may relate the black hole thermodynamics with the properties of the conformal field theory (CFT) using the

In this paper, we are going to take into account the corrections to the thermodynamics of a

The metric of a

For a

Now we are going to define an intrinsic temperature for large modified black holes by identifying probes with radiation particles in the vicinity of the horizon of the black hole. Using the radiation photons with average energy

To find the black hole temperature, it is necessary to introduce the specific forms of the functions

By substituting

In the case of

In the case of

As an important point, one may conclude that the predicted entropy within our formalism is smaller than that of the standard Bekenstein-Hawking entropy while the predicted temperature within our formalism is greater than that of the standard one. Furthermore, the entropy and the temperature of the black hole can be derived for any other dimensionality in the same manner. By continuing the procedure for higher dimensionality, one can deduce that the appearance of the logarithmic correction term in the entropy-area relation is restricted to even black hole dimensionality. In fact, if one tries to consider the higher order correction terms for different values of

On the other hand, the modified dispersion relation is not confined only to rainbow gravity. In other words, MDR is a common feature to most of the quantum gravity candidates and, in particular, to the study of loop quantum gravity (LQG) and of models based on noncommutative geometry. In fact there has been strong interest in modifications to the energy-momentum dispersion relation [

The well-known Cardy formula gives the entropy of a 2-dimensional CFT as

Within rainbow gravity, by using equation

In the case

In the case

In 2-dimensional conformal field theory, when the conformal weight of the ground state is zero, the valid form of C-V formula is

In the case of

In the case of

We have computed the thermodynamical properties of a

The author declares that there is no conflict of interests regarding the publication of this paper.

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