Black Holes in the Ghost Condensate
Shinji Mukohyama
TL;DR
The paper investigates how a ghost condensate reacts to black holes, showing that when $X$ is near the Higgs-like scale $M^4$ the condensate behaves like a geodesic dust and accretion into large black holes is highly suppressed. By formulating the theory with an action $I=\int d^4x\sqrt{-g}[P(X)-{\alpha(\Box\phi)^2}/{2M^2}]$ and treating higher-derivative effects perturbatively in $\epsilon=\alpha/(M^2 r_g^2)$, the authors derive a small accretion rate for the approximate $X=M^4$ solution and confirm this remains true even when including the $\alpha$ term. They also analyze the case with nonzero $P'$, showing that if the ghost condensate energy density behaves like dark matter, the induced accretion onto a black hole grows only as $\sim (H_0 v)^2$, still remaining slow. The work reconciles the ghost condensate with dark matter-like behavior and emphasizes the importance of backreaction, countering prior claims of large accretion by demonstrating its suppression for sufficiently large black holes and cosmological contexts.
Abstract
We investigate how the ghost condensate reacts to black holes immersed in it. A ghost condensate defines a hypersurface-orthogonal congruence of timelike curves, each of which has the tangent vector u^μ=-g^{μν}\partial_νφ. It is argued that the ghost condensate in this picture approximately corresponds to a congruence of geodesics. In other words, the ghost condensate accretes into a black hole just like a pressure-less dust. Correspondingly, if the energy density of the ghost condensate at large distance is set to an extremely small value by cosmic expansion then the late-time accretion rate of the ghost condensate should be negligible. The accretion rate remains very small even if effects of higher derivative terms are taken into account, provided that the black hole is sufficiently large. It is also discussed how to reconcile the black hole accretion with the possibility that the ghost condensate might behave like dark matter.