Entropic force between two horizons of dilaton black holes with a power-Maxwell field

Abstract

In this paper, we consider (n+1)-dimensional topological dilaton de Sitter black holes with power-Maxwell field as thermodynamic systems. The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon respectively are interrelated. So the total entropy of the space-time should be the sum of the entropies of the black hole horizon and the cosmological horizon plus a corrected term which is produced by the association of the two horizons. We analyze the entropic force produced by the corrected term at given temperatures, which is affected by parameters and dimensions of the space-time. It is shown that the change of entropic force with the position ratio of two horizons in some region is similar to that of Lennard-Jones force with the position of particles. If the effect of entropic force is similar to that of Lennard-Jones force, and other forces are absent, the motion of the cosmological horizon relative to the black hole horizon would have an oscillating process. The entropic force between the two horizons is probably one of the participants to drive the evolution of universe.

Continuous Phase Transition of the higher-dimensional topological de-Sitter Spacetime with the Non-linear Source

“…In addition, authors [30] had added scalar hair to the dS black hole to ensure equilibrium between two horizons, where only a reverse Hawking-Page transition is possible and the total entropy is the sum of two horizons (i.e., ignoring the interaction between two horizons). On this basis, people proposed the total entrapy in a dS spacetime in the thermodynamic equilibrium should contain the interaction between two horizons [31][32][33][34][35]. From this viewpoint, we will investigate the thermodynamic phase transition for a dS spacetime with non-linear source as an ordinary thermodynamic system in the thermodynamic equilibrium.…”