Thermodynamics of dilaton black holes charged with a higher-dimensional Coulomb-like field

Abstract

AbstractThe field equations are written explicitly in the framework of higher-dimensional Einstein-dilaton gravity theory, which is coupled to non-linear electrodynamics. It is proved that this theory is confronted with the problem of indeterminacy. By this we mean that the number of unknowns is one more than the unique differential equations. Analytical solutions are obtained by the use of power-law and exponential ansatz functions, separately. It is found that this theory in the presence of a Coulomb-like electric field, inspired by non-linear electrodynamics, admits two novel classes of black hole solutions for each of the ansatz functions. Under the influence of the dilaton field, the asymptotic behavior of the solutions is neither flat nor anti-de Sitter. Through comparison of the results it is shown that, under some simple conditions, both of the ansatz functions lead to the same results. It is illustrated that our exact solutions can produce two-horizon, one-horizon, and horizonless black holes. The validity of the first law of black hole thermodynamics is investigated by use of a Smarr-type mass formula. The thermal stability of the black holes is analyzed by making use of the canonical ensemble and geometrical methods, separately. The results of these two alternative approaches are compared by the use of plots.