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

TL;DR

This paper proposes a method to construct regular black holes, wormholes, and gravastars by gluing exterior spacetimes to a regular interior with a tube-like geometry, avoiding singularities and apparent horizons.

Contribution

It introduces a novel class of composite spacetimes with regular interiors and specific horizon structures, expanding the landscape of non-singular compact objects in general relativity.

Findings

Inner regions are regular and supported by vacuum-like matter.

Composite spacetimes can have horizons without apparent horizons.

Wormholes are static, non-traversable, and do not violate null energy condition.

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 $p_{r}+\rho =0$ where $p_{r}=T_{r}^{r}$ is the longitudinal pressure, $\rho =-T_{0}^{0}$ is the energy density, $T_{\mu}^{\nu}$ 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.