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

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.

Final version published on General Relativity Gravitation

References in corpus (7)

• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Entropic Accelerating Universe
• Cosmological expansion and local physics
• Cosmological apparent and trapping horizons
• Black Hole Evaporation in an Expanding Universe
• The Hawking temperature of expanding cosmological black holes
• Graceful exit from inflation to radiation era with rapidly decreasing agegraphic potentials

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