Gravitational Pressure, apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity

Abstract

In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann-Lemaitre-Robertson-Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation $T_{A}dS_{A} = dE_{A}+P_{A}dV_{A}$ at the apparent horizon, where $E_{A}$ is the total energy inside the apparent horizon, $V_{A}$ is the areal volume of the apparent horizon, $P_{A}$ is the radial pressure over the apparent horizon area, $S_{A}$ is the entropy which can be assumed as one quarter of the apparent horizon area only for a non stationary apparent horizon. We identify $T_{A}$ as the temperature at the surface of the apparent horizon. We shown that for all expanding accelerated FLRW model of universe the radial pressure is positive.