Accretion of Ghost Condensate by Black Holes

TL;DR

This work investigates whether ghost condensates can be efficiently accreted by black holes by modeling the condensate as an irrotational fluid with a non-minimal kinetic term and solving for steady-state, spherically symmetric accretion onto a Schwarzschild black hole. The accretion rate is shown to be set by the theory's energy scale $M$, not by the ambient cosmological density, and the flow exhibits a transonic solution for $A<1$ with a flux-coefficient bounded between 1 and about 2.6 (approaching dust-like behavior as $A\to1$). If $M$ is as large as ~10 MeV, the implied accretion could be astrophysically significant, imposing tight constraints on the model; for smaller $M$ the rate is reduced but backreaction and non-steady effects remain important. Overall, the results place nontrivial constraints on ghost condensate scenarios as dark matter or infrared-modified gravity and highlight the need for further study of backreaction, time evolution, and stability in realistic settings.

Abstract

The intent of this letter is to point out that the accretion of a ghost condensate by black holes could be extremely efficient. We analyze steady-state spherically symmetric flows of the ghost fluid in the gravitational field of a Schwarzschild black hole and calculate the accretion rate. Unlike minimally coupled scalar field or quintessence, the accretion rate is set not by the cosmological energy density of the field, but by the energy scale of the ghost condensate theory. If hydrodynamical flow is established, it could be as high as tenth of a solar mass per second for 10MeV-scale ghost condensate accreting onto a stellar-sized black hole, which puts serious constraints on the parameters of the ghost condensate model.

Figures (3)

• Figure 1: Ghost condensate kinetic term (top) and equivalent fluid description (bottom). Equation of state $w$ and sound speed $c_s^2$ are shown by dashed and solid curves, respectively.
• Figure 2: Flow diagrams $v(x)$ of the ghost condensate accretion onto a black hole for $A=3/4$ (left) and $A=1$ (right). Inflow, no-flow, and (unstable) outflow branches are shown by solid, dot-dash, and dotted lines correspondingly. Flow trajectories passing through the critical point are emphasized by thicker lines. Negative $v$ region corresponds to reversed flow direction, and is not shown.
• Figure 3: Dependence of the accretion rate coefficient $\alpha$ on $A$.