MG11 
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N-spheres: regular black holes without apparent horizons, static wormholes with event horizons and gravastars with a tube-like core

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. When the surface of gluing approaches the horizon, surface stresses vanish. 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. 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.

Distorted Killing horizons and algebraic classification of curvature tensors

We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned on the horizon. It is also pointed out that results obtained in the tetrad adjusted to a static observer in general differ from those obtained in a free-falling frame. This is connected to the fact that a static observer becomes null on the horizon. It is also shown that finiteness of the Kretschmann scalar on the horizon is compatible with the divergence of some Weyl component in the freely falling frame. We call such new objects ‘truly naked black holes’.

Boulware state and exactly solvable models of 2D dilaton gravity

We discuss self-consistent geometries and behavior of dilaton in exactly solvable models of 2D dilaton gravity, with quantum fields in the Boulware state. If the coupling $H(\phi)$ between curvature and dilaton $\phi$ is non-monotonic, backreaction can remove the classical singularity. As a result, an everywhere regular star-like configuration may appear, in which case the Boulware state (contrary to expectations) smooths out the system. For monotonic $H(\phi)$ exact solutions confirm the features found before with the help of numerical methods: the appearance of the bouncing point and the presence of isotropic singularity at the classically forbidden branch of the dilaton.