Cosmological coupled black holes immersed in dark sector

Abstract

Motivated by theoretical and observational developments of cosmological coupled black holes, we construct an exact analytical solution for a black hole immersed in an anisotropic dark sector background, adopting the framework established by [Cadoni et al., JCAP 03 (2024) 026]. By generalizing a static seed metric to a dynamical FLRW background, we derive a solution where the black hole mass co-evolves with the cosmic expansion. We then obtain the explicit form of the radius-dependent coupling exponent, revealing that the interaction is governed by the dark halo profile. Considering the ubiquity of the dark halos surrounding supermassive black holes, our model provides a potential realization of cosmological coupling, interpreting the mass growth as the dynamical response of the surrounding dark sector fluid to the Hubble flow, distinct from the method of modifying the black hole's internal equation of state.

Figures (3)

• Figure 1: The normalized relation of static horizon radius $r_+$ versus density parameter $\lambda$.
• Figure 2: The density parameter $\lambda$ versus the coupling exponent $k(r)$ at a fixed coordinate radius. The lines do not cross at the starting point because in the Schwarzschild limit $\lambda\rightarrow 0$, $k(r)_{\lambda\to0}\sim\frac{2M}{r-2M}$, i.e. $k\sim2$ for $r=3M$ and $k\sim1$ for $r=4M$.
• Figure 3: Numerical evolution of the apparent horizon. Left Panel: The normalized comoving radius versus static event horizon $r_{\rm AH}/r_+$ as a function of the scale factor. Right Panel: The normalized physical areal radius versus static event horizon $R_{\rm AH}/r_+$, showing the global increase of BHs. Note that at the present epoch $a=1$, the normalized horizon radius slightly deviates from the point $(1, 1)$. This is because we assume a non-static universe with initial expansion rate $H\neq0$. In the strict static limit $H\rightarrow0$, the ratio asymptotically converges to exactly $1$.