Holographic Principle bounds on Primordial Black Hole abundances

TL;DR

This paper combines thermodynamics and the Holographic Principle to derive upper bounds on primordial black hole abundances in the early universe, providing constraints independent of traditional flux-based limits.

Contribution

It introduces a novel method using the Holographic Principle and thermodynamics to set bounds on primordial black hole densities during early cosmological epochs.

Findings

Derived maximum black hole mass inside a spherical box with radiation.

Established critical thresholds for black hole formation from radiation.

Provided strong constraints on primordial black hole density, independent of flux-based limits.

Abstract

The generalized Second Law of thermodynamics and the Holographic Principle are combined to obtain the maximum mass of black holes formed inside a static spherical box of size $R$ filled with radiation at initial temperature $T_{i}$. The final temperature after the formation of black holes is evaluated, and we show that a critical threshold exists for the radiation to be fully consumed by the process. We next argue that if some form of Holographic Principle holds, upper bounds to the mass density of PBHs formed in the early universe may be obtained. The limits are worked out for inflationary and non-inflationary cosmological models. This method is independent of the known limits based on the background fluxes (from cosmic rays, radiation and other forms of energy) and applies to potentially important epochs of PBH formation, resulting in quite strong constraints to $\Omega_{pbh}$.