Merging Black Holes’ Entropy Surpasses Totality, New Cosmological Budget Advances Understanding

Scientists are revising our understanding of the universe’s total entropy, revealing black holes as surprisingly dominant contributors.Siyuan Chen (Center for Astrophysics | Harvard & Smithsonian and Vanderbilt University), Karan Jani (Vanderbilt University), and Thomas W. Kephart (Vanderbilt University) et al. present a new cosmological entropy budget, incorporating the impact of merging black holes detected through gravitational waves. Their research demonstrates that entropy generated by these mergers may have exceeded that of the cosmic microwave background in the early universe, fundamentally altering our view of the thermodynamic state of the cosmos. This work, utilising population synthesis models and numerical relativity, also suggests a potential ‘entropy floor’ established by primordial black hole mergers in the Dark Ages and highlights a significant thermodynamic asymmetry in black hole merger events , generating immense entropy despite relatively inefficient gravitational-wave energy production.

This breakthrough research, utilising population synthesis models and phenomenological fits derived from numerical relativity, focuses on black holes within the stellar to lite-intermediate-mass range, specifically, those spanning 5 to 300 solar masses, originating from supernovae or binary mergers. The study reveals three key insights into the role of black holes in shaping the universe’s entropy, challenging previous assumptions about the dominance of relic radiation. Researchers meticulously calculated the cumulative entropy generated by merging black holes, finding it surpasses the total entropy from cosmic microwave background photons around redshift z∼12, coinciding with the onset of the Over-massive Black Hole Galaxy phase.

The team achieved a refined estimate of the total cosmological entropy, integrating the latest findings from gravitational-wave astronomy and cosmological observations to provide a comprehensive inventory of black hole populations. Experiments show that if primordial black holes constitute even a small fraction of dark matter, their early binary mergers establish an “entropy floor” in the Dark Ages, potentially dominating the cumulative merger-generated entropy history. This suggests a previously underestimated contribution of primordial black holes to the universe’s early thermodynamic state. Furthermore, the work establishes a thermodynamic asymmetry in black hole mergers, highlighting that the production of gravitational-wave energy is remarkably inefficient compared to the immense generation of Bekenstein-Hawking entropy, a fundamental measure of a black hole’s disorder.
This research builds upon decades of work estimating cosmic entropy, but incorporates recent gravitational-wave observations from the LIGO-Virgo-KAGRA collaboration, which have revealed a previously unknown black hole mass range. The study categorises stellar-origin black holes into standard stellar black holes (5, 45 M⊙), PISN black holes (45, 130 M⊙), and lite-intermediate-mass black holes (130, 300 M⊙), allowing for a more nuanced analysis of their individual entropy contributions. By expressing the Bekenstein-Hawking formula in terms of mass and spin, scientists computed the entropy of individual black holes and then extrapolated these values to estimate the total entropy contributed by black hole populations across cosmic time. The study unveils that black holes contain more entropy than any other component of the observable universe, solidifying their crucial role in the universe’s thermodynamic progression and the arrow of time.

By computing cosmological density parameters, the researchers demonstrate that black hole mergers are a significant, yet energetically inefficient, source of entropy, with the vast majority of energy being radiated as gravitational waves rather than contributing to the overall disorder of the universe. This breakthrough opens new avenues. Researchers employed population synthesis models and phenomenological fits derived from numerical relativity to accurately estimate black hole entropy contributions. To calculate individual black hole entropy, the team harnessed the Bekenstein-Hawking Formula, expressing it in terms of mass (m) and spin (a) as S = kAc2 4Għ2 = 2πkG ħc m2(1 + p 1 −a2).

They categorized stellar-origin black holes into three regimes: standard stellar BHs (5, 45 M⊙), PISN BHs (45, 130 M⊙), and lite-IMBHs (130, 300 M⊙), allowing for precise entropy calculations across different mass ranges. The total number density of black hole progenitors was determined using the Salpeter Initial Mass Function (IMF) with a power-law index of α = 2.35+0.35 −0.65, calibrated to match the observed present-day cosmic stellar mass density of Ω⋆ ≃0.0027 ±0.0005. Experiments integrated the SEVN stellar evolution code, assuming a low-metallicity environment (Z = 2 × 10−4) to model massive black hole formation, accounting for PPISN and PISN effects. The research team innovatively addressed the non-bijective mapping between progenitor and remnant masses by enforcing particle number conservation, computing the remnant mass function ξBH(mrem) by summing IMF contributions from disjoint progenitor intervals.

A uniform distribution for the dimensionless spin parameter, a ∼U[0, 1], was assumed to calculate entropy for each remnant mass, generating distributions of remnant count and total entropy. Furthermore, the study calculated entropy changes for merging binary black holes (BBHs) using data from the LIGO and Virgo collaborations, specifically posterior samples obtained with the IMRPhenomXPHM waveform model. Four entropy types were calculated: primary (S1), secondary (S2), remnant (Sf), and merger-produced (∆S), where ∆S = Sf −(S1 + S2). This detailed analysis revealed that cumulative entropy from merging black holes surpasses the total entropy from the cosmic microwave background around a redshift of, suggesting a significant role for mergers in shaping the early universe’s thermodynamic state.

Black hole mergers dominate the universal entropy budget

Scientists have revealed that black holes collectively possess more entropy than all other components of the observable universe. Recent gravitational-wave observations from the LIGO and Virgo collaborations have identified a previously unknown range of black hole masses, prompting a crucial update to the cosmological entropy budget. The research team meticulously calculated increases in entropy resulting from binary black hole mergers, aligning with the principles of the second law of thermodynamics, and incorporated these findings into a revised budget. Experiments revealed that the cumulative entropy from merging black holes exceeds the total entropy from the cosmic microwave background around a redshift of, indicating a more significant role for mergers in shaping the thermodynamic state of the early universe than previously thought.

Data shows that this threshold occurs at the onset of the Over-massive Black Hole Galaxy phase, fundamentally altering our understanding of early cosmic evolution. The team measured entropy using the Bekenstein-Hawking formula, expressing it in terms of black hole mass and spin, and categorised stellar-origin black holes into standard stellar BHs (5, 45 M⊙), PISN BHs (45, 130 M⊙), and lite-IMBHs (130, 300 M⊙). Researchers discovered that if primordial black holes constitute a non-zero fraction of dark matter, their early binary mergers establish an “entropy floor” in the Dark Ages. Tests prove that even small abundances of primordial black holes can dominate the cumulative merger-generated entropy history.

The study highlights a thermodynamic asymmetry in black hole mergers, where the production of gravitational-wave energy is inefficient compared to the immense generation of Bekenstein-Hawking entropy. Measurements confirm that the team integrated a Salpeter Initial Mass Function with a power-law index of α = 2.35+0.35 −0.65 to compute the total number density of massive stars collapsing into black holes. Furthermore, the work provides updated assessments of entropy contributions from both known and previously overlooked components, including intermediate-mass black holes. Scientists computed remnant mass functions using the SEVN stellar evolution code, assuming a low-metallicity environment (Z = 2 × 10−4) to account for the formation of massive black holes. For 168 binary black hole events reported by the LIGO-Virgo-Kagra (LVK) collaboration, the team calculated entropy changes (∆S) using the IMRPhenomXPHM waveform model and posterior samples from the GW Open Science Center. Results demonstrate that event-level ∆S measurements reveal a correlation between redshift and entropy change during mergers, with the purple-shaded region corresponding to the dark energy-dominated era (z ≤ 0.5).

AmerBlack hole mergers dominate early universe entropy

Scientists have revised the cosmic entropy budget, quantifying contributions from stellar-collapse black holes and their mergers. This research integrates gravitational-wave observations with population synthesis models to map black hole entropy across cosmic time, revealing a surprising thermodynamic history of the universe. The study demonstrates that the cumulative entropy from merging black holes exceeds that of the cosmic microwave background around the onset of the Over-massive Black Hole Galaxy phase at redshift 12, indicating a significant role for mergers in the early universe’s thermodynamic state. Researchers found that even a small population of primordial black holes could establish an “entropy floor” during the Dark Ages, potentially dominating the overall entropy generated by mergers.

Furthermore, the analysis highlights a thermodynamic asymmetry in black hole mergers, a large generation of Bekenstein-Hawking entropy despite inefficient gravitational-wave energy production. The authors acknowledge limitations in extrapolating merger rates at high redshifts, beyond the current reach of ground-based detectors. Future gravitational wave facilities, including space-based observatories like LISA and proposed mid-band concepts such as LILA, will be crucial for empirically verifying these predictions and precisely reconstructing entropy production in the universe’s earliest epochs.