Narrow Results

In this paper, we study the solutions of Einstein’s field equations in Einstein–Maxwell-dilaton gravity. By presenting the (3+1)-dimensional action in which gravity is coupled to a dilaton field, we derive the field equations. We present a new class of charged dilaton black hole solutions in Einstein–Maxwell-dilaton theory and investigate the effects of dilaton field on the properties of space–time. We show that these solutions are physical and describe spherically symmetric charged black holes. The calculated potential is Liouville type and has two rules. The exact solution of the field equations leads to the production of the metric function with three rules. By examining the physical properties of the solutions, we find the mass, charge, electric potential and temperature of charged dilaton black holes. Also, with the help of the canonical ensemble method, we study the thermodynamics and thermal stability of solutions and show the effects of dilaton and Maxwell fields on the thermodynamics of these solutions. Finally, by examining the phase transition of the solutions, we present thermal stability of the black hole in (3+1)-dimensional.

In this paper, we argue that once quantum gravitational effects change the classical geometry of a black hole and remove the curvature singularity, the black hole would not evaporate entirely but approach a remnant. In a modified Schwarzschild spacetime characterized by a finite Kretschmann scalar, a minimal mass of the black hole is naturally bounded by the existence of the horizon rather than introduced by hand. A thermodynamical analysis discloses that the temperature, heat capacity and the luminosity vanish naturally when the black hole mass approaches the minimal value. This phenomenon may be attributed to the existence of the minimal length in quantum gravity. It can also be understood heuristically by connecting the generalized uncertainty principle with the running of Newton's gravitational constant.