Survival of black holes through a cosmological bounce

We analyze whether a black hole can exist and survive in a universe that goes through a cosmological bounce. To this end, we investigate a central inhomogeneity embedded in a bouncing cosmological background modeled by the comoving generalized McVittie metric. Contrary to other dynamical metrics available in the literature, this solution allows for the interaction of the central object with the cosmological fluid. We show that the horizons associated with this metric change with cosmic time because they are coupled to the cosmic evolution as the mass of the central object is always proportional to the scale factor: it decreases during contraction and increases during expansion phases. After a full analysis of the causal structure of this spacetime, we determine that a dynamical black hole persists during the contraction, bounce, and expansion of the universe. This result implies that there is a class of bouncing models that admits black holes at all cosmological epochs. If these models are a correct approximation to the real universe, then black holes surviving a cosmic collapse could play some role in the subsequent expanding phase.

Figure 1

The blue and red lines indicates the conditions ${\theta }_{\mathrm{out}}=0$ and ${\theta }_{\mathrm{in}}=0$, respectively. The white zones point out the regular regions of the spacetime (${\theta }_{\mathrm{in}}{\theta }_{\mathrm{out}}<0$), the light pink zone the antitrapped region (${\theta }_{\mathrm{in}}{\theta }_{\mathrm{out}}>0$, with ${\theta }_{\mathrm{out}}>0$ and ${\theta }_{\mathrm{in}}>0$), and the light blue zone marks the trapped region (${\theta }_{\mathrm{in}}{\theta }_{\mathrm{out}}>0$, with ${\theta }_{\mathrm{out}}<0$ and ${\theta }_{\mathrm{in}}<0$). The dashed green line denotes the surface $R=2r_{g}a(T)$. Here, $T_b={10}^{-4}\mathrm{s}$ and $m_0=10M_{\odot }$.

Figure 2

The blue and red lines indicates the conditions ${\theta }_{\mathrm{out}}=0$ and ${\theta }_{\mathrm{in}}=0$, respectively. The dashed green line denotes the surface $\tilde{r}=2r_g$. Here, $T_b={10}^{-4}\mathrm{s}$ and $m_0=10M_{\odot }$.

Figure 3

The blue and red lines indicates the conditions ${\theta }_{\mathrm{out}}=0$ and ${\theta }_{\mathrm{in}}=0$, respectively. The dashed green line denotes the surface $\tilde{r}=2r_g$. The trapped regions are painted in light blue, the antitrapped are colored in light pink and the regular zones are in white. Here, $T_0={10}^{-4}\mathrm{s}$ and $m_0=10M_{\odot }$.

Figure 4

The dotted (dashed) curves represent the null ingoing (outgoing) radial geodesics. The grey shadow regions show some light cones and the black arrow indicates the future direction. Here, $T_b={10}^{-4}\mathrm{s}$ and $m_0=10M_{\odot }$.

Figure 5

Light cone structure close to the surface $x=2$. The dotted (dashed) curves represent the null ingoing (outgoing) radial geodesics. The grey shadow regions show some light cones and the black arrow indicates the future direction. Here, $T_b={10}^{-4}\mathrm{s}$ and $m_0=10M_{\odot }$.

Figure 6

Qualitative Penrose diagram of the CGMcV spacetime for a bouncing cosmological model in the expanding region ($t>0$). The dotted lines represent null ingoing geodesics while the dashed lines null outgoing geodesics. The gray shadow region corresponds to the black hole interior. Here, ${\mathcal{J}}^{+}$ represents the future null infinity.

Figure 7

Qualitative Penrose diagram of the CGMcV spacetime for a bouncing cosmological model in the contracting region ($t<0$). The dotted lines represent null ingoing geodesics while the dashed lines null outgoing geodesics. The gray shadow region corresponds to the black hole interior. Here, ${\mathcal{J}}^{-}$ represents the past null infinity.