Black Holes in the Turbulent Phase of Viscous Rip Cosmology

Abstract

We study the phantom fluid in the late universe, thus assuming the equation of state parameter $w$ to be less than $-1$. The fluid is assumed to consist of two components, one laminar component $ρ$ and one turbulent component $ρ_T$, the latter set proportional to $ρ$ as well as to the Hubble parameter, $ρ_T =3τHρ$ with $τ$ a positive constant associated with the turbulence. The effective energy density is taken to be $ρ_e= ρ+ ρ_T$, and the corresponding effective pressure is $p_e=w ρ_e$, with $w$ constant. These basic assumptions lead to a Big Rip universe; the physical quantities diverging during a finite rip time $t_s$. We then consider the mass accretion of a black hole in such a universe. The most natural assumption of setting the rate $dM/dt$ proportional to $M^2$ times the sum $ρ_e+p_e$, leads to a negative mass accretion, where $M(t)$ goes to zero linearly in $(t_s-t)$ near the singularity. The Hubble parameter diverges as $(t_s-t)^{-1}$, whereas $ρ_e$ and $p_e$ diverge as $(t_s-t)^{-2}$. We also discuss other options and include, for the sake of comparison, some essential properties of mass accretion in the early (inflationary) universe.

7 pages latex 2e, no figures; to appear in Int. J. Geom. Meth. Mod. Phys