[Paper Review] Black holes embedded in FLRW cosmologies

Rudeep Gaur, Matt Visser|arXiv (Cornell University)|Aug 14, 2023

Astrophysical Phenomena and ObservationsPhysics and Astronomy3 citations

TL;DR

This paper critically examines claims that black holes directly grow due to cosmological expansion, independent of accretion or mergers. By analyzing exact solutions—Kottler, McVittie, and Kerr–de Sitter—it demonstrates no such coupling exists, as these solutions show no mass increase from expansion, undermining the proposed mechanism and highlighting a fundamental scale separation between black hole and cosmological physics.

ABSTRACT

There has recently been some considerable interest expressed in a highly speculative model of black hole evolution -- allegedly by a postulated direct coupling between black holes and cosmological expansion independently of accretion or mergers. We wish to make several cautionary comments in this regard -- at least three exact solutions corresponding to black holes embedded in a FLRW background are known, (Kottler, McVittie, Kerr-de Sitter), and they show no hint of this claimed effect -- thereby implying that this claimed effect (if it exists at all) is certainly nowhere near ubiquitous.

Motivation & Objective

• To evaluate the physical plausibility of claims that black hole mass increases due to direct coupling with cosmological expansion, independent of accretion or mergers.
• To examine whether known exact solutions of Einstein's equations—specifically Kottler, McVittie, and Kerr–de Sitter—exhibit any such mass growth effect.
• To highlight the enormous separation of scales between galactic black hole physics (milli-parsec scale) and cosmological dynamics (gigaparsec scale), which makes such direct coupling implausible.
• To critique the theoretical framework underpinning the claimed effect, particularly the flawed assumption that a black hole gas mimics dark energy.
• To reinforce the conclusion that observed black hole evolution is best explained by standard processes like accretion and mergers, not by a novel coupling to expansion.

Proposed method

• Analysis of three exact solutions to Einstein's equations: Schwarzschild–de Sitter (Kottler), Schwarzschild–FLRW (McVittie), and Kerr–de Sitter, all embedding black holes in expanding FLRW backgrounds.
• Use of coordinate transformations to examine the asymptotic behavior of these solutions, particularly in the large-$r$ limit, to assess whether black hole mass couples to the cosmological expansion parameter $H$.
• Derivation of the metric expansion for Kerr–de Sitter spacetime, showing that the mass parameter $m$ and cosmological constant $H$ remain independent, with no cross-term coupling.
• Evaluation of the scale separation between black hole physics ($r \lesssim 10^{-3}$ parsec) and cosmological homogeneity scale ($\gtrsim 10^8$ parsecs), introducing a natural transition scale $r_* = \sqrt[3]{m / \rho_{\text{FLRW}}}$.
• Comparison of the theoretical framework in reference [1] with established GR solutions, identifying inconsistencies such as the incorrect assumption that black hole mass fractions produce pressure equivalent to dark energy.
• Use of observational bounds from [8] and other studies to constrain the claimed effect, finding it excluded at $\sim 3\sigma$ and compatible with zero at $\sim 1\sigma$.

Experimental results

Research questions

• RQ1 Do exact solutions of Einstein's equations that embed black holes in FLRW cosmologies—such as Kottler, McVittie, and Kerr–de Sitter—exhibit any direct coupling between black hole mass and cosmological expansion?
• RQ2 Is the claimed mechanism of black hole mass increase due to cosmological expansion, independent of accretion or mergers, physically supported by known exact solutions in general relativity?
• RQ3 What is the role of the scale separation between galactic black hole physics (milli-parsec scale) and cosmological dynamics (gigaparsec scale) in assessing the plausibility of such a coupling?
• RQ4 Does the theoretical framework proposed in reference [1], which suggests black hole gas mimics dark energy, hold up under scrutiny in the context of known exact solutions?
• RQ5 Can the observed cosmological energy density contribution from black holes at redshift $z \leq 7$ be explained by a direct coupling to expansion, or is it better accounted for by standard astrophysical processes?

Key findings

• The Kottler (Schwarzschild–de Sitter), McVittie (Schwarzschild–FLRW), and Kerr–de Sitter solutions—three exact solutions embedding black holes in expanding FLRW spacetimes—show no evidence of black hole mass growth due to cosmological expansion.
• In the Kerr–de Sitter solution, the mass parameter $m$ and the Hubble parameter $H$ remain independent constants; no coupling term appears in the metric expansion at large $r$.
• The asymptotic behavior of these exact solutions confirms that black hole spacetimes approach de Sitter space at large distances, with no modification of the black hole mass due to the cosmological constant or expansion rate.
• The natural scale $r_* = \sqrt[3]{m / \rho_{\text{FLRW}}}$ separates regions dominated by black hole physics from those dominated by cosmological expansion, reinforcing the physical implausibility of direct coupling.
• Observational constraints from [8] exclude the claimed effect at $\sim 3\sigma$, and are consistent with zero effect at $\sim 1\sigma$, further undermining the proposed mechanism.
• The theoretical framework in reference [1], which posits that black hole mass fractions produce pressure equivalent to dark energy, is shown to be flawed, as a black hole gas behaves like dust, not dark energy.