Dynamics of black holes in de Sitter spacetimes

Nonlinear dynamics in cosmological backgrounds has the potential to teach us immensely about our Universe, and also to serve as prototype for nonlinear processes in generic curved spacetimes. Here we report on dynamical evolutions of black holes in asymptotically de Sitter spacetimes. We focus on the head-on collision of equal mass binaries and for the first time compare analytical and perturbative methods with full blown nonlinear simulations. Our results include an accurate determination of the merger/scatter transition (consequence of an expanding background) for small mass binaries and a test of the cosmic censorship conjecture, for large mass binaries. We observe that, even starting from small separations, black holes in large mass binaries eventually lose causal contact, in agreement with the conjecture.

Figure 1

Conformal factor $\chi$ for a single BH evolution with $H=0.8H_{\mathrm{crit}}$ using the McVittie slicing condition, Eq. (10). The obtained numerical results are plotted, along the $z$ coordinate (symmetry $\chi (-z)=\chi (z)$ imposed at $z=0$), against the expected analytical solutions (solid lines).

Figure 2

Critical coordinate distance for small mass binaries, from both initial data and dynamical evolutions, as well as a point particle estimate, as a function of $H/H_{\mathrm{crit}}$. We obtain this estimate from the coordinate distance to the horizon, Eq. (4), for a particular value of $m$. The $t=0$ line refers to the critical separation between having or not having a common BAH in the initial data. The inset shows details of the approach to the critical line for $H=0.6H_{\mathrm{crit}}$, where $a$ is an acceleration parameter.

Figure 3

Hamiltonian constraint violation along the $z$-axis at time $t=48m$ for a simulation with $H=0.9H_{\mathrm{crit}}$ and initial distance $d=0.8m$.

Figure 4

Proper distance between the BH horizons as a function of time for the $H=0.9H_{\mathrm{crit}}$, and initial (coordinate) distance $d\simeq 0.9m$. The two holes stay at approximately constant distance up to $t\approx 8m$ after which cosmological expansion starts dominating.

Figure 5

Snapshots at different times (from left to right $t/m=0.0$, 8.0156, 20.016) of a simulation with $H=1.05H_{\mathrm{crit}}$, and an initial coordinate distance $d/m=1.5002$. The dotted blue line denotes the CAH (for an observer at $z=0$) which is first seen in this simulation at $t/m=8.0156$, highly distorted. At late times, the CAH has an areal radius of $R=4.94876$, while the “theoretical value” for pure dS is $R=1/H=4.94872$, a remarkable agreement showing spacetime is accurately empty dS for the observer at $z=0$ and the BHs are not in causal contact.