N-spheres in general relativity: Regular black holes without apparent horizons, static wormholes with event horizons and gravastars with a tube-like core

Abstract

We consider a way to avoid black hole singularities by gluing a black hole exterior to an interior with a tube-like geometry consisting of a direct product of two-dimensional AdS, dS, or Rindler spacetime with a two-sphere of constant radius. As a result we obtain a spacetime with either "cosmological" or "acceleration" (event) horizons but without an apparent horizon. The inner region is everywhere regular and supported by matter with the vacuum-like equation of state p r + ρ = 0 where p r = T r r is the longitudinal pressure, ρ = −T 0 0 is the energy density, T ν µ is the stress-energy tensor. When the surface of gluing approaches the horizon, surface stresses vanish, while p r may acquire a finite jump on the boundary. Such composite spacetimes accumulate an infinitely large amount of matter inside the horizon but reveal themselves for an external observer as a sphere of a finite ADM mass and size.If the throat of the inner region is glued to two black hole exteriors, one obtains a wormhole of an arbitrarily large length. Wormholes under discussion are static but not traversable, so the null energy condition is not violated. In particular, they include the case with an infinite proper distance to the throat. We construct also gravastars with an infinite tube as a core and traversable wormholes connected by a finite tube-like region.

Traversable wormholes: Minimum violation of the null energy condition revisited

“…It does not mean that such configurations have no physical sense. By contrary, in some situations it is the tubelike configurations which are placed to the forefront (for example, in the context of the problem of avoidance singularities [12], in investigating properties of phantom matter [14], etc.). However, in any case, they represent a special class of wormhole configurations which differ from the standard ones.…”

“…In principle, one can take a finite piece of this horn and glue it to the metric with dr dl > 0 on the right side and dr dl < 0 on the left side. In doing so, one can obtain so-called "null wormholes" (N-wormholes) [12]. Although inside the region where p r + ρ = 0 NEC is satisfied on the verge, gluing to the normal matter on the borders needs the presence of exotic material and we return to the situation under discussion with all corresponding difficulties.…”

Hiding Charge in a Wormhole

“…Let us note that wormholes with "tube-like" structure (and regular black holes with "tube-like" core) have been previously obtained within different contexts in refs. [41][42][43][44][45][46][47][48][49].…”

“…Substituting again (48), (45) into the matching relations (41) --(43) we find for the wormhole parameters:…”

Gravastar solutions with continuous pressures and equation of state

“…In [9] gravastar solutions have been studied in a generalized (Reissner-Nordström) exterior and solutions of the model stemming from the original Mazur-Mottola model have been analyzed. Gravastar type solutions in the context of solutions to Einstein's equations with tube-like cores have also been recently considred [10]. Pioneering in-depth studies of spherically symmetric systems with deSitter asymptotics may be found in [11] - [14].…”