Entropy, energy and temperature-length inequality for Friedmann universes

Abstract

In this paper we continue the study of the physical consequences of our modified black hole entropy formula in expanding spacetimes. In particular, we apply the new formula to apparent horizons of Friedmann expanding universes with zero, negative and positive spatial curvature. As a first result, we found that, apart from the static Einstein solution, the only Friedmann spacetimes with constant (zero) internal energy are the ones with zero spatial curvature. This happens because, in the computation of the internal energy $U$, the contribution due to the non-vanishing Hubble flow must been added to the usual Misner-Sharp energy giving, for zero curvature spacetimes, a zero value for $U$. This fact does not hold when curvature is present. After analyzing the free energy $F$, we obtain the correct result that $F$ is stationary only for physical systems in isothermal equilibrium, i.e. a de Sitter expanding universe. This result permits us to trace back a physically reasonable hypothesis concerning the origin of the early and late times de Sitter phase of our universe. Finally, we deduce an interesting temperature-length inequality similar to the time-energy uncertainty of ordinary quantum mechanics but with temperature instead of time coordinate. Remarkably, this relation is independent on the gravitational constant $G$ and can thus be explored also in non gravitational contexts.

Typos fixed,journal reference updated, Final version published on IJMPD

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Cited by in corpus (9)

• Axial and polar gravitational wave equations in a de Sitter expanding universe by Laplace transform
• A statistical representation of the cosmological constant from finite size effects at the apparent horizon
• On a physical description and origin of the cosmological constant
• A proposal for the thermodynamics of certain open systems
• Building a linear equation of state for trapped gravitons from finite size effects and the Schwarzschild black hole case
• Statistical description of massless excitations within a sphere with a linear equation of state and the dark energy case
• The physical origin of the cosmological constant: continuum limit and the analogy with the Casimir effect
• A possible new cosmological redshift effect due to $\Lambda$ on traveling gravitational waves in Friedmann universes
• The 3D perturbed Schrödinger Hamiltonian in a Friedmann flat spacetime testing the primordial universe in a non commutative spacetime