Phase transition and entropic force of de Sitter black hole in massive gravity

TL;DR

This paper studies the thermodynamics and phase transitions of de Sitter black holes in massive gravity, revealing a surprising similarity between entropic forces and Lennard-Jones interactions, with implications for cosmic acceleration.

Contribution

It introduces effective thermodynamic quantities for de Sitter black holes in massive gravity and analyzes their phase transitions and entropic forces, linking black hole physics to cosmological acceleration.

Findings

Effective thermodynamic quantities are derived for dS black holes in massive gravity.

Phase transition conditions for these black holes are established.

Entropic force behavior resembles Lennard-Jones force between particles.

Abstract

It is well known that de Sitter(dS) black holes generally have a black hole horizon and a cosmological horizon, both of which have Hawking radiation. But the radiation temperature of the two horizons is generally different, so dS black holes do not meet the requirements of thermal equilibrium stability, which brings certain difficulties to the study of the thermodynamic characteristics of black holes. In this paper, dS black hole is regarded as a thermodynamic system, and the effective thermodynamic quantities of the system are obtained. The influence of various state parameters on the effective thermodynamic quantities in the massive gravity space-time is discussed. The condition of the phase transition of the de Sitter black hole in massive gravity space-time is given. We consider that the total entropy of the dS black hole is the sum of the corresponding entropy of the two horizons plus an extra term from the correlation of the two horizons. By comparing the entropic force of interaction between black hole horizon and the cosmological horizon with Lennard-Jones force between two particles, we find that the change rule of entropic force between the two system is surprisingly the same. The research will help us to explore the real reason of accelerating expansion of the universe.