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

Bjørn Jensen·Svend E. Hjelmeland
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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

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Bjørn Jensen, Svend E. Hjelmeland. 1996-09-23. A stringy black string and a stringy black hole in four dimensions. https://arxiv.org/abs/gr-qc/9608068

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