First law of thermodynamics for dynamical apparent horizons and the entropy of Friedmann universes

TL;DR

This paper extends the first law of thermodynamics to dynamical apparent horizons in Friedmann universes, revealing a universal constant total energy that supports the holographic principle.

Contribution

It introduces a generalized internal energy and distinguishes dynamical temperature, providing new insights into the thermodynamics of expanding universe horizons.

Findings

The internal energy at the apparent horizon is a constant of motion.

Total energy of a flat universe at the apparent horizon is a universal constant, possibly zero.

Supports the holographic principle through thermodynamic analysis.

Abstract

Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. In this letter, we begin the study of this new formula to obtain the first law of thermodynamics for dynamical apparent horizons. In this regard we obtain a generalized expression for the internal energy $U$ together with a distinction between the dynamical temperature $T_D$ of apparent horizons and the related one due to thermodynamics formulas. Remarkable, when the expression for $U$ is applied to the apparent horizon of the universe, we found that this internal energy is a constant of motion. Our calculations thus show that the total energy of our spatially flat universe including the gravitational contribution, when calculated at the apparent horizon, is an universal constant that can be set to zero from simple dimensional considerations. This strongly support the holographic principle.