Abstract
In this paper, we present charged dilatonic black holes in gravity's rainbow. We study geometric and thermodynamic properties of black hole solutions. We also investigate the effects of rainbow functions on different thermodynamic quantities for these charged black holes in dilatonic gravity's rainbow. Then, we demonstrate that first law of thermodynamics is valid for these solutions. After that, we investigate thermal stability of the solutions using canonical ensemble and analyze the effects of different rainbow functions on thermal stability. In addition, we present some arguments regarding the bound and phase transition points in context of geometrical thermodynamics. We also study the phase transition in extended phase space in which cosmological constant is treated as the thermodynamic pressure. Finally, we use another approach to calculate and demonstrate that obtained critical points in extended phase space are representing a second order phase transition for these black holes.
Highlights
It has been demonstrated that gravity’s rainbow is related to Horava–Lifshitz gravity [14]. This is because both of these theories are based on modifying 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
It may be noted that such a modification of the usual energy-momentum has been obtained in discrete spacetime [15], spacetime foam [16], the spin-network in loop quantum gravity (LQG) [17], ghost condensation [18], and non-commutative geometry [19,20]
It may be noted that various other approaches to quantum gravity indicate that the Lorentz symmetry might only be an effective symmetry which occurs in the IR limit of some fundamental theories of quantum gravity [29,30,31,32,33]
Summary
It may be noted that the UV modification of the usual energy-momentum dispersion relation implies the breaking of the Lorentz symmetry in the UV limit of the theory. The evaporation of quantum black holes has been investigated using two-dimensional dilaton gravity [60,61] Motivated by these applications, we analyze the dilaton field using the formalism of gravity’s rainbow. The thermodynamical critical behavior of black holes in the presence of different matter fields and gravities has been investigated in the literature [91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109] Another interesting method of studying the thermodynamical structure of black holes is through the use of geometry. We study the stability of such solutions in gravity’s rainbow and phase transition of these black holes through the heat capacity, geometrical thermodynamics, and the analogy between the cosmological constant and the thermodynamical pressure.
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