Cosmological energy in a thermo-horizon and the first law

TL;DR

This paper examines the thermodynamics of a cosmological horizon called the thermo-horizon, highlighting a contradiction in the energy law which is resolved by adopting a Gibbs' equation for a vacuum-like component.

Contribution

It introduces a new perspective on the thermodynamics of cosmological horizons by replacing the first law with a Gibbs' equation to resolve energy definition contradictions.

Findings

Contradiction between the first law and total energy definition.

Replacing the first law with Gibbs' equation resolves the contradiction.

Thermo-horizon obeys Bekenstein-Hawking entropy and temperature.

Abstract

We consider a cosmological horizon, named thermo-horizon, to which are associated a temperature and an entropy of Bekenstein-Hawking and which obeys the first law for an energy flow calculated through the corresponding limit surface. We point out a contradiction between the first law and the definition of the total energy contained inside the horizon. This contradiction is removed when the first law is replaced by a Gibbs' equation for a vacuum-like component associated to the event horizon.