A stringy black string and a stringy black hole in four dimensions

TL;DR

This paper constructs four-dimensional black string and black hole solutions from three-dimensional BTZ black holes, revealing a separation mechanism that helps exclude naked singularities in Einstein theory with negative cosmological constant.

Contribution

It introduces a novel uplift of BTZ solutions to four dimensions, leading to new black string and black hole solutions with a separation mechanism that clarifies the exclusion of naked singularities.

Findings

Derived four-dimensional black string and black hole solutions from BTZ black holes.

Identified a separation mechanism that excludes naked singularities in three-dimensional Einstein theory.

Generalized the BTZ solution using the separation mechanism.

Abstract

We uplift the static three dimensional black hole solution found by Banados, Teitelboim and Zanelli (BTZ) into four dimensional space time. In this way we obtain a black string solution with a relativistic string source, as well as a new black hole solution which is also generated by a relativistic ``stringy'' source. It is shown that when passing continuously from the region of the one dimensional parameter spaces which characterize these solutions, containing naked singular strings or naked singular ``points'', and into the region containing black strings or black holes, the metrics ``blow up'' at a critical point in both parameter spaces. We show that a similar ``separation'' mechanism can be introduced in three dimensions. In this way we also obtain a generalization of the BTZ solution. The ``separation'' mechanism, and its immediate consequences, offers an hitherto missing technical argument needed in order to exclude the naked singularities (the ``mass gap'') from the space of ``physically permissible'' solutions in three dimensional Einstein theory coupled to a negative cosmological constant. PACS nos.: 04.40.Nr, 04.20.Cv