Time-independent wormholes

Abstract

We study two-sided static wormholes with an exact Killing symmetry that translates both mouths of the wormhole toward the future. This differs from the familiar Kruskal wormhole whose time translation is future-directed only in one asymptotic region and is instead past-directed in the other. Our spacetimes are solutions to Einstein-Hilbert gravity sourced by scalar domain walls. Explicit examples are found in the thin wall approimation. More generally, we show that such spacetimes can arise in the presence of scalar fields with potentials that are C 1 but not C 2 and find examples numerically. However, solutions with an exact such Killing symmetry are forbidden when the scalar potential is smooth. Finally, we consider the mutual information of boundary regions associated with such wormholes in AdS/CFT. Although the interior of our solutions are unstable, we find that even mutual informations between opposite boundaries are already thermalized at any finite t in the sense that they agree with the t → ∞ limit of results from the familiar AdS-Kruskal solution.

A perturbative perspective on self-supporting wormholes

“…This 5-dimensional spacetime is usually Kaluza-Klein reduced along a different Killing field and then interpreted as a 4-dimensional spacetime sourced by a magnetic field[44,45]. Since the energy of the solution is fixed by Noether's theorem independent of the reduction, the results of[44,45] show that the reduction used here gives a 4d solution with positive tension (rescaled from[44,45] by the relative length of their Kaluza-Klein circle relative to ours) but which in our case is 4d vacuum except at the string singularity on the z-axis 12. Indeed, since this example breaks rotational symmetry it may be that both cases become traversable, with traversability being achieved along different generators for each of the two boundary conditions.…”

“…Since the spacetime is static and smooth, it also supports a Hartle-Hawking state defined by the Euclidean path integral. Thus the analysis of section 2 applies and -barring a miraculous general cancellation -at least for generic values of parameters the wormhole must become traversable under first-order back-reaction from either periodic or anti-periodic scalar fields 12 .…”

Complexity growth of rotating black holes with a probe string

“…A candidate of its solution is firewalls [20,21,22]. Complexity is realized as an important quantity for studying the structure of black hole spacetime -the Einstein-Rosen bridge [23,24,25,26,27,28,29,30,31], which is a structure of connecting two external black holes thought to be equivalent to entangled pair of particles (ER = EPR) [32]. Especially, complexity is thought to be a good tool of diagnosing the existence of firewalls [31].…”

A scale dependent black hole in three-dimensional space–time

“…This proves the statement claimed earlier, that for fixed values of ǫ, G 0 , ℓ 0 the limit of M 0 → ∞ implies, according to (48), that the physical mass grows without bound as M ∼ M 0 → ∞, and nevertheless the horizon converges to the finite distance given in (35). Since our initial input was the condition ( 14), it would be very interesting to analyse this result in future studies in the context of the "Quantum Null Energy Conjecture" [75][76][77][78][79].…”