Does a wormhole survive a cosmological bounce?

Abstract

We investigate whether a dynamical wormhole could survive in a universe that undergoes a cosmological bounce. First, the conditions under which a wormhole could persist from a contracting to an expanding phase of the cosmos are presented. Then, the only two known cosmological solutions of Einstein's equations representing wormholes are analyzed, and it is shown that both dynamical wormholes exist for all cosmic times on both sides of a bouncing universe and at the bounce itself. We also provide a detailed analysis of the causal structure of such spacetimes and the matter content of the wormhole. Finally, some possible astrophysical manifestations of surviving wormholes in a bouncing universe are mentioned. Our results show that, at least for the Kim and Pérez-Raia Neto solutions, there is no topology change in the chosen cosmological model with a bounce.

Figures (13)

• Figure 1: Plot of expression \ref{['fc']} as a function of the cosmic time for $b_0 = 10, 22.21, 40 \; G M_{\odot} /c^2$.
• Figure 2: Plot of expression \ref{['flaring-out-cond-kim']} as a function of the cosmic time for $b_0 = 20, 30, 40 \; G M_{\odot} /c^2$.
• Figure 3: Plot of the areal radius of the throat for Kim wormhole as a function of the cosmic time (blue line). The red curve represents the minimum value of the areal radius coordinate.
• Figure 4: Plot of the causal structure of the Kim wormhole solution. The red (blue) curves represent the null ingoing (outgoing) radial geodesics. The grey shaded regions show some light cones and the black arrow indicates the future direction. The black curve corresponds to the location of the throat. The dashed black curves show the points at which the condition $dR/dt = 0$ is satisfied. We adopt $T_b = 10^{-4}$ and $b_0 = 10 \; G M_{\odot} /c^2$.
• Figure 5: Embedding diagram for the Kim wormhole for $t/T_{\rm {b}} =-100, -10, 0, 10, 100$ (from left to right). We adopt $b_0 = 10 \; G M_{\odot} /c^2$.