Holography, Cosmology and the Second Law of Thermodynamics

TL;DR

This paper explores the relationship between holography and thermodynamics in cosmological settings, proposing that the generalized second law better describes entropy bounds in dynamic universes, especially beyond simple models.

Contribution

It introduces a generalized second law framework that extends holographic principles to complex, time-dependent cosmological spacetimes, highlighting where traditional holography applies or fails.

Findings

The generalized second law aligns with holography in simple isotropic universes.

In complex spacetimes, holographic bounds need modification based on thermodynamics.

Holographic bounds are not straightforward in closed universes or black hole horizons.

Abstract

We propose that in time dependent backgrounds the holographic principle should be replaced by the generalized second law of thermodynamics. For isotropic open and flat universes with a fixed equation of state, the generalized second law agrees with the cosmological holographic principle proposed by Fischler and Susskind. However, in more complicated spacetimes the two proposals disagree. A modified form of the holographic bound that applies to a post-inflationary universe follows from the generalized second law. However, in a spatially closed universe, or inside a black hole event horizon, there is no simple relationship that connects the area of a region to the maximum entropy it can contain.