Does the mass of a black hole decrease due to the accretion of phantom energy?

According to Babichev et al., the accretion of a phantom test fluid onto a Schwarzschild black hole will induce the mass of the black hole to decrease, however the backreaction was ignored in their calculation. Using new exact solutions describing black holes in a background Friedmann-Robertson-Walker universe, we find that the physical black hole mass may instead increase due to the accretion of phantom energy. If this is the case, and the future universe is dominated by phantom dark energy, the black hole apparent horizon and the cosmic apparent horizon will eventually coincide and, after that, the black hole singularity will become naked in finite comoving time before the big rip occurs, violating the cosmic censorship conjecture.

Figure 1

The black hole apparent horizon (solid line) increases while the cosmic apparent horizon (dotted line) decreases with the accretion of phantom energy onto the black hole. There is a time at which the two horizons coincide and after which both horizons disappear and the black hole singularity becomes a naked singularity. The plots correspond to the equation of state parameter $w=-2$.

Figure 2

The black hole apparent horizon (solid line) increases, while the cosmic apparent horizon (dotted line) decreases with the divergence of the phantom field. There is a moment at which the two horizons coincide and after which they disappear, the black hole singularity becoming naked. These plots correspond to $\alpha =-3$, $t_0=1$, $M=1$.

Figure 3

The black hole apparent horizon (lower line) first decreases and then increases, while the cosmic apparent horizon (upper line) always increases in the dust-dominated Universe. There was a moment at which the two horizons coincided and before which the singularity was naked. The plots correspond to $M_0=0.8$, $a_0=1$.

Figure 4

The Penrose-Carter diagram for a phantom-dominated universe with a black hole. The diagram is similar to the one for the Schwarzschild solution except for two sections removed and two cosmic singularities added. For brevity, we only label the black hole singularity (BHS), white hole singularity (WHS), big bang singularity (BBS), and big rip singularity (BRS) in the diagram. The black hole apparent horizon (BAH) and cosmic apparent horizon (CAH) are also shown.

Figure 5

The Penrose diagram for a dust-dominated universe with a black hole. This diagram also coincides with the one for the Schwarzschild solution, except for two sections removed and two cosmic singularities added. We only label the black hole singularity (BHS), white hole singularity (WHS), big bang singularity (BBS), and big crunch singularity (BCS) in the diagram. The black hole apparent horizon (BAH) and cosmic apparent horizon (CAH) are also shown.