Charged Banados-Teitelboim-Zanelli Black Hole Research Articles

Weak cosmic censorship conjecture for the (2+1)-dimensional charged BTZ black hole in the Einstein–Gauss–Bonnet Gravity

It is well known that (2+1) dimensional charged BTZ (Banados, Teitelboim, Zanelli) black hole can be overcharged by a charged scalar field and a charged particle in contrast to their analogues in (3+1) and higher dimensions. In this regard, it may play an important role to understand more deeply the properties of the (2+1)-dimensional charged black hole in the Einstein–Gauss–Bonnet (EGB) gravity. In this paper, we test the validity of the weak cosmic censorship conjecture for the (2+1)-dimensional charged black hole in novel EGB theory derived recently by Henniger et al. (2021). We show that the minimum energy that particle can have at the horizon becomes negative for both an extremal and nearly-extremal BTZ black holes in EGB gravity. It is proven that both extremal and nearly-extremal (2+1) dimensional BTZ black hole could be overcharged in EGB theory, leading to the violation of the weak cosmic censorship conjecture (WCCC), which is in good agreement with the results obtained for the classical BTZ black hole.

BPS-like bound and thermodynamics of the charged BTZ black hole

The charged Ba\~nados-Teitelboim-Zanelli (BTZ) black hole is plagued by several pathologies: (a) Divergent boundary terms are present in the action; hence, we have a divergent black-hole mass. (b) Once a finite, renormalized, mass $M$ is defined, black-hole states exist for arbitrarily negative values of $M$. (c) There is no upper bound on the charge $Q$. We show that these pathological features are an artifact of the renormalization procedure. They can be completely removed by using an alternative renormalization scheme leading to a different definition ${M}_{0}$ of the black-hole mass, which is the total energy inside the horizon. The new mass satisfies a BPS-like bound ${M}_{0}\ensuremath{\ge}\frac{\ensuremath{\pi}}{2}{Q}^{2}$, and the heat capacity of the hole is positive. We also discuss the black-hole thermodynamics that arises when ${M}_{0}$ is interpreted as the internal energy of the system. We show, using three independent approaches (black-hole thermodynamics, Einstein equations, and Euclidean action formulation), that ${M}_{0}$ satisfies the first law if a term describing the mechanical work done by the electrostatic pressure is introduced.

Thermodynamic critical and geometrical properties of charged BTZ black hole

The heat capacities and the electric capacitances of charged Ba\~nados-Teitelboim-Zanelli (BTZ) black hole are first calculated. By using the equilibrium fluctuation theory of thermodynamics the second-order moments in three different ensembles are obtained, and it is found that in the microcanonical ensemble the extremal charged BTZ black hole is a critical point of the second-order phase transition. The critical exponents associated with some response coefficients satisfy the scaling law of the first kind and the effective spatial dimension is determined to be one from the scaling law of the second kind. The Ricci curvature scalar associated with the Ruppeiner thermodynamic metric is calculated, which suggests also that the effective spatial dimension of the charged BTZ black hole is one.

Thermodynamics of Einstein-Born-Infeld black holes in three dimensions

We show that all thermodynamic quantities of the Einstein-Born-Infeld black holes in three dimensions can be obtained from the dilaton and its potential of two-dimensional dilaton gravity through dimensional reduction. These are all between nonrotating uncharged BTZ (Banados-Teitelboim-Zanelli) black hole (NBTZ) and charged BTZ black hole (CBTZ).

Near-horizon limit of the charged BTZ black hole and AdS2quantum gravity

We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, near-horizon AdS_2 geometry with constant dilaton and U(1) field and an asymptotic AdS_2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS_2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown-Hennaux-like boundary deformations and near-horizon excitations. The central charge c_as of the asymptotic CFT is determined by 3D Newton constant G and the AdS length l, c_as=3l/G, whereas that of the near-horizon CFT also depends on the U(1) charge Q, c_nh \propto l Q/\sqrt G.