Effective Pressure of the FRW Universe

Abstract

In this paper, we study the effective pressure of the $N$-dimensional FRW(Friedmann-Robertson-Walker) universe in Einstein gravity, Gauss-Bonnet gravity, and Lovelock gravity. The effective pressure is defined by $P_{eff}:=-dE/dV$, where $E=\rho V$ is the effective energy and $V$ is the volume of the FRW universe inside the apparent horizon. The effective pressure in Einstein gravity is always negative and its absolute value decreases with the horizon radius $R_A$. The effective pressure in Gauss-Bonnet gravity is different with the one in Einstein gravity only when $N\ge 6$. In this case, if $\alpha >0$, the effective pressure is always negative, but if $\alpha <0$, it is not always negative and has a minimum. The effective pressure in Lovelock gravity can have multiple zero-points and extreme points. The effective pressure in different dimensions has interesting relations. We also find that under certain condition, the effective pressure is equivalent with the `ordinary' pressure $p$ of the perfect fluid, and this condition do not depend on the specific choice of gravitational theories.

arXiv comment9 pages,2 figures

References in corpus (9)

• Unified first law of black-hole dynamics and relativistic thermodynamics
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• The minus sign in the first law of de Sitter horizons
• The P-V Phase Transition of the FRW Universe
• First Principle Study of Gravitational Pressure and Thermodynamics of FRW Universe
• Phase Transitions and Critical Phenomena for the FRW Universe in an Effective Scalar-Tensor Theory
• Equation of State and Joule-Thomson Expansion for the FRW Universe in the Brane World Scenario
• Thermodynamics of the arbitrary dimensional FRW universe: Joule-Thomson expansion