Regularization ambiguity and van der Waals black hole in 2+1 dimensions

Abstract

Charged black holes in a ($2+1$)-dimensional anti-de Sitter space-time suffer from some limitations such as the ambiguity in the definition of the mass and the bad short distance behavior. In this paper we present a way to resolve such issues. By extending the parameter space of the BTZ geometry, we properly identify the integration constants in order to remove the conical singularity sitting at the origin. In such a way we obtain a well defined Minkowski limit and horizons also in the case of de Sitter background space. On the thermodynamic side, we obtain a proper internal energy, by invoking the consistency with the Area Law, even if the mass parameter does not appear in the metric coefficients. As a further improvement, we show that it is sufficient to assume a finite size of the electric charge to obtain a short scale regular geometry. The resulting solution, generalizing the charged BTZ metric, is dual to a van der Waals gas.

18 pages, 3 figures, version published on EJPC

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• Non-commutative geometry inspired higher-dimensional charged, black holes
• Charged rotating noncommutative black holes
• Black holes in an ultraviolet complete quantum gravity
• Noncommutative Inspired Black Holes in Extra Dimensions
• Regular black hole in three dimensions
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Cited by in corpus (2)

• Noncommutative black holes in extended anti-de Sitter phase space
• Planckian charged black holes and their cosmological ramifications