Accretion of Generalized Chaplygin Gas onto Cosmologically Coupled Black Holes

TL;DR

This work investigates how a cosmological dark fluid, modeled as Generalized Chaplygin Gas, accretes onto black holes embedded in an expanding universe described by the McVittie metric. A perturbative backreaction framework is developed to track how accretion alters the effective mass and the evolution of both black hole and cosmological apparent horizons, yielding analytic expressions for horizon dynamics in matter-dominated and de Sitter-like epochs. The results reveal a subtle interplay: in a matter-dominated era, backreaction can delay horizon formation despite more available accreting matter, while in a de Sitter regime, horizon formation timing depends on the background density and can shift in the opposite direction. These findings illuminate the coupling between local accretion processes and global expansion, with potential implications for primordial black holes and dark-sector cosmology.

Abstract

We study the accretion of cosmic dark fluids, responsible for driving the accelerated expansion of the universe, onto cosmologically coupled black holes. More specifically, we focus on the accretion of the Generalized Chaplygin Gas (GCG). To incorporate the global features of the GCG into this analysis, we employ the McVittie metric, which describes a black hole embedded in an expanding cosmological background. Within this framework, accretion is studied while consistently accounting for the backreaction on the metric components. Using a perturbative approach, we derive an expression for the effective black hole mass and for the evolution of both the black hole and cosmological apparent horizons under accretion. The analysis is performed in two distinct cosmological regimes: first, a matter-dominated era, and subsequently, a de Sitter era. In both cases, it is possible to determine analytically the instant in which accretion begins. For the matter-dominated era, the analytical expression shows that the greater the amount of matter available for accretion, the longer the accretion takes to start.

Figures (3)

• Figure 1: Apparent black hole and cosmological horizon formation time as a function of $A$ (solid lines), as given by (\ref{['t0ac matter']}). The dashed line represent the instant of formation of the apparent horizons without available matter for accretion, $t_{0}$, given by \ref{['t0']}. The mass parameter $M_{0}$ is set to $1$. We also consider $\alpha=0.1$.
• Figure 2: Temporal evolution of the apparent black hole horizon without available matter for accretion (solid black line) and with available matter for accretion (colored solid lines); and of the cosmological horizons without available matter for accretion (black dashed line) and with available matter for accretion (colored dashed lines) for different values of $A$. The mass parameter $M_{0}$ is set to $M_{0}=1$, such that $t$ is measured in units of $M_{0}$. Also, we consider $\alpha=0.1$.The horizontal dashed line represents the asymptote $r=2M_{0}$. The vertical solid line represents the instant $t_{0}$ at which the horizons form in the case without accretion, as given by Eq. (\ref{['t0']}).
• Figure 3: Apparent black hole and cosmological horizon formation time as a function of $A$, as given by (\ref{['t0 DE']}). We consider $\alpha=0.1$, $B=1-A$ and $k=0.39$.