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

Charged black holes in a ($$2+1$$ 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.

Fix the dual geometries of $$T\bar{T}$$ deformed CFT$$_2$$ and highly excited states of CFT$$_2$$

In previous works, we have developed an approach to fix the leading behaviors of the pure AdS$$_3$$ 3 and BTZ black hole from the entanglement entropies of the free CFT$$_2$$ 2 and finite temperature CFT$$_2$$ 2 , respectively. We exclusively use holographic principle only and make no restriction about the bulk geometry, not only the kinematics but also the dynamics. In order to verify the universality and correctness of our method, in this paper, we apply it to the $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 , which breaks the conformal symmetry. In terms of the physical arguments of the $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 , the derived metric is a deformed BTZ black hole. The requirement that the CFT$$_2$$ 2 lives on a conformally flat boundary leads to $$r_{c}^{2}=\ 6R_{AdS}^{4}/(\pi c\mu )$$ r c 2 = 6 R AdS 4 / ( π c μ ) naturally, in perfect agreement with previous conjectures in literature. The energy spectum and propagation speed calculated with this deformed BTZ metric are the same as these derived from $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 . We furthermore fix the dual geometry of highly excited states with our approach. The result contains the descriptions for the conical defect and BTZ black hole.

(2 + 1)-dimensional dynamical black holes in Einstein-nonlinear Maxwell theory

Radiative extensions of BTZ metric in 2 + 1 dimensions are found which are sourced by nonlinear Maxwell fields and a null current. This may be considered as generalization of the problem formulated long go by Vaidya and Bonnor. The mass and charge are functions of retarded/advanced null coordinate apt for decay/inflation. The new solutions are constructed through a Theorem that works remarkably well for any nonlinear electrodynamic model. Hawking temperature is analyzed for the case of the Born–Infeld electrodynamics.