A braneworld puzzle about entropy bounds and a maximal temperature

TL;DR

This paper explores the saturation of entropy bounds at a maximal temperature in cosmology and AdS/CFT frameworks, suggesting black hole production as a key factor, but finds no conclusive mechanism to prevent exceeding this temperature.

Contribution

It links entropy bounds saturation to black hole production at a maximal temperature and analyzes the issue using both cosmological and AdS/CFT models, highlighting unresolved mechanisms.

Findings

Entropy bounds are saturated at T_max=M_Planck/N^1/2 in four dimensions.

Black hole production occurs at T_max, potentially explaining entropy saturation.

Known mechanisms are insufficient to prevent the universe from surpassing T_max.

Abstract

Entropy bounds applied to a system of N species of light quantum fields in thermal equilibrium at temperature T are saturated in four dimensions at a maximal temperature T_max=M_Planck/N^1/2. We show that the correct setup for understanding the reason for the saturation is a cosmological setup, and that a possible explanation is the copious production of black holes at this maximal temperature. The proposed explanation implies, if correct, that N light fields cannot be in thermal equilibrium at temperatures T above T_max. However, we have been unable to identify a concrete mechanism that is efficient and quick enough to prevent the universe from exceeding this limiting temperature. The same issues can be studied in the framework of AdS/CFT by using a brane moving in a five dimensional AdS-Schwarzschild space to model a radiation dominated universe. In this case we show that T_max is the temperature at which the brane just reaches the horizon of the black hole, and that entropy bounds and the generalized second law of thermodynamics seem to be violated when the brane continues to fall into the black hole. We find, again, that the known physical mechanisms, including black hole production, are not efficient enough to prevent the brane from falling into the black hole. We propose several possible explanations for the apparent violation of entropy bounds, but none is a conclusive one.