Abstract
In this paper, we combine Lovelock gravity with gravity's rainbow to construct Lovelock gravity's rainbow. Considering the Lovelock gravity's rainbow coupled to linear and also nonlinear electromagnetic gauge fields, we present two new classes of topological black hole solutions. We compute conserved and thermodynamic quantities of these black holes (such as temperature, entropy, electric potential, charge and mass) and show that these quantities satisfy the first law of thermodynamics. In order to study the thermal stability in canonical ensemble, we calculate the heat capacity and determinant of the Hessian matrix and show in what regions there are thermally stable phases for black holes. Also, we discuss the dependence of thermodynamic behavior and thermal stability of black holes on rainbow functions. Finally, we investigate the critical behavior of black holes in the extended phase space and study their interesting properties.
Highlights
It is important to understand the UV behavior of general relativity, and various attempts have been made to obtain the UV completion of general relativity such that it reduces to the general relativity in the IR limit
Such a UV completion has been studied for geometries that occur in the type IIA string theory [3] and type IIB string theory [4]
The Horava-Lifshitz gravity is based on a deformation of the usual energy-momentum dispersion relation in the UV limit, such that it reduces to the usual energy-momentum dispersion relation in the IR limit
Summary
It is important to understand the UV behavior of general relativity, and various attempts have been made to obtain the UV completion of general relativity such that it reduces to the general relativity in the IR limit. Motivated by the development of the Horava-Lifshitz gravity, the UV completion of various geometric structures in the string theory has been studied by taking a different Lifshitz scaling for space and time. Such a UV completion has been studied for geometries that occur in the type IIA string theory [3] and type IIB string theory [4]. It has been observed that this can have interesting phenomenological consequences [47] Motivated by these subjects, we will analyze the black holes in Lovelock gravity’s rainbow coupled to the Maxwell field, and extend our investigations to the case of nonlinear electrodynamics.
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