Humanly traversable wormholes

We point out that there can be humanly traversable wormhole solutions in some previously considered theories for physics beyond the Standard Model, namely the Randall-Sundrum model.

Figure 1

(a) We see a sketch of the geometry of a single extremal black hole. It develops a long throat with a locally ${\mathrm{AdS}}_2\times S^2$ geometry. (b) The wormhole geometry. We start with two separate throats and we connect them. The geometry of the connected throats is again ${\mathrm{AdS}}_2\times S^2$. The two mouths of the wormhole are at some distance $d$. The red brackets indicates the region of overlapping validity of the metrics (2.4) and (2.7). The green lines denote the magnetic field lines. They form closed circles, entering one mouth, traveling through the wormhole, exiting the other mouth and then going back to the first mouth in the ambient space.

Figure 2

(a) We display the topology of the full five-dimensional space. It is essentially filling the space “outside” the wormhole in the ambient space. We highlighted a special slice that ends on a particular magnetic field line. (b) We display IR part of the geometry of the highlighted slice. This geometry is a portion of global ${\mathrm{AdS}}_3$, the time direction is perpendicular to the page and we plot just the spatial direction. The beyond the drawn region, the geometry goes over to the ${\mathrm{AdS}}_5$ geometry as it approaches the Planck brane. The part of the magnetic field line that is outside the wormhole was colored purple. For each magnetic field line, or each point on the $S^2$ we have a slice like this.

Figure 3

We show the numerical solution describing the flow. We have ${\mathrm{AdS}}_5$ at large $\rho$, where $\sigma \sim \lambda \sim \rho +\text{constant}$. For negative $\rho$ this goes to $\sigma \sim 0$ and ${\lambda }^{\prime }=\sqrt{3}$. Besides plotting $\sigma$ and $\lambda$ we plotted the approximations that are valid when $|\rho |$ is large.