Cosmological Budget of Entropy from Merging Black Holes

TL;DR

This paper updates the cosmological entropy budget of black holes, revealing that mergers significantly contributed to the universe's entropy, surpassing relic radiation, and highlighting the role of primordial black holes in early universe thermodynamics.

Contribution

It provides a new comprehensive update on black hole entropy contributions, including effects of mergers and primordial black holes, using population synthesis and numerical relativity.

Findings

Merging black holes' entropy exceeds cosmic microwave background entropy at z~12.

Primordial black hole mergers set an entropy floor during the Dark Ages.

Black hole mergers produce more entropy than gravitational-wave energy, indicating thermodynamic asymmetry.

Abstract

Black holes contain more entropy than any other component of the observable universe. Gravitational-wave observations from LIGO and Virgo have shown evidence of a previously unknown black hole mass range, which provides new information to update the entropy budget. Increases in entropy due to binary black hole mergers, as implied in the second law of thermodynamics, should also be added to the budget. In this study, we update the cosmological entropy budget for black holes in the stellar to lite-intermediate-mass range $(5-300~M_\odot)$, originating from either supernovae or binary mergers, by utilizing a suite of population synthesis models and phenomenological fits derived from numerical relativity. We report three new insights: Firstly, the cumulative entropy from merging black holes surpasses the total entropy from cosmic microwave background photons around the onset of the Over-massive Black Hole Galaxy phase at $z\sim 12$, suggesting that mergers played a more significant role in shaping the thermodynamic state of the early universe than relic radiation. Secondly, if primordial black holes constitute a nonzero fraction of dark matter, their early binary mergers establish an ``entropy floor" in the Dark Ages and can dominate the cumulative merger-generated entropy history even for small abundances. Thirdly, by computing the cosmological density parameters, we highlight the thermodynamic asymmetry in black hole mergers, where the production of gravitational-wave energy is inefficient compared to the immense generation of Bekenstein-Hawking entropy.