Cosmological wormholes

Motivated by the cosmological wormhole solutions obtained from our recent numerical investigations, we provide a definition of a wormhole which applies to dynamical situations. Our numerical solutions do not have timelike trapping horizons but they are wormholes in the sense that they connect two or more asymptotic regions. Although the null energy condition must be violated for static wormholes, we find that it can still be satisfied in the dynamical context. Two analytic solutions for a cosmological wormhole connecting two Friedmann universes without trapping horizons are presented.

Figure 1

The causal structure of the self-similar solution with dark energy which is asymptotically Friedmann at one end and (quasi-)Friedmann at the other. $t=0$ corresponds to the initial singularity, while ${\Im }_1^{+}$ and ${\Im }_2^{+}$ correspond to two distinct null infinities. CEH stands for cosmological event horizon. The spacetime is asymptotically quasi-Kantowski-Sachs spacetime around the wormhole throat [17].

Figure 2

The causal structure of the Friedmann-Friedmann cosmological wormhole spacetime with thin shells for $1/3<\gamma <(14-2\sqrt{19})/9$. $t=0$ corresponds to the initial singularity, while ${\Im }_1^{+}$ and ${\Im }_2^{+}$ correspond to two distinct null infinities. The thick curves correspond to two massive thin shells with negative surface energy density. The whole spacetime is foliated by trapped surfaces and there is no trapping horizon.

Figure 3

The causal structure of the cosmological Ellis wormhole spacetime (4.53) for $a=t/t_0$. $t=0$ corresponds to the null initial singularity, while ${\Im }_1^{+}$ and ${\Im }_2^{+}$ correspond to two distinct null infinities. The thin straight line corresponds to the wormhole throat $x=0$. For $t_0<2b$, the whole spacetime is foliated by trapped surfaces and there is no trapping horizon. For $t_0\le b$, the dominant energy condition is satisfied.