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Register a new userThe BTZ black hole with a time-dependent boundary
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The non-rotating BTZ solution is expressed in terms of coordinates that allow for an arbitrary time-dependent scale factor in the boundary metric. We provide explicit expressions for the coordinate transformation that generates this form of the metric, and determine the regions of the complete Penrose diagram that are convered by our parametrization. This construction is utilized in order to compute the stress-energy tensor of the dual CFT on a time-dependent background. We study in detail the expansion of radial null geodesic congruences in the BTZ background for various forms of the scale factor of the boundary metric. We also discuss the relevance of our construction for the holographic calculation of the entanglement entropy of the dual CFT on time-dependent backgrounds.
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We consider gedanken experiments to destroy an extremal or near-extremal BTZ black hole by throwing matter into the horizon. These black holes are vacuum solutions to (2+1)-dimensional gravity theories, and are asymptotically $mathrm{AdS}_3$. Provided the null energy condition for the falling matter, we prove the following---(i) in a Mielke-Baekler model without ghost fields, when torsion is present, an extremal BTZ black hole can be overspun and becomes a naked conical singularity; (ii) in 3-dimensional Einstein gravity and chiral gravity, which both live in torsionless limits of Mielke-Baekler model, an extremal BTZ black hole cannot be overspun; and (iii) in both Einstein gravity and chiral gravity, a near-extremal BTZ black hole cannot be overspun, leaving the weak cosmic censorship preserved. To obtain these results, we follow the analysis of Sorce and Wald on their gedanken experiments to destroy a Kerr-Newman black hole, and calculate the second order corrections to the black hole mass. Furthermore, Walds type of gedanken experiment provides an operational procedure of proving the third law of black hole mechanics. Through the AdS/CFT correspondence, our results on BTZ black holes also indicate that a third law of thermodynamics holds for the holographic conformal field theories dual to 3-dimensional Einstein gravity and chiral gravity.
We show that the nonlinear $sigma-$model in an asymptotically $AdS_3$ space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear $sigma-$model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear $sigma-$model fields and changes the space-time metric, and it can be used to map an extremal $BTZ$ black hole to infinitely many hairy black hole solutions.
We obtain rotating black hole solutions to the novel 3D Gauss-Bonnet theory of gravity recently proposed. These solutions generalize the BTZ metric and are not of constant curvature. They possess an ergoregion and outer horizon, but do not have an inner horizon. We present their basic properties and show that they break the universality of thermodynamics present for their static charged counterparts, whose properties we also discuss. Extending our considerations to higher dimensions, we also obtain novel 4D Gauss-Bonnet rotating black strings.
In this paper we analyze some interesting features of the thermodynamics of the rotating BTZ black hole from the Carath{e}odory axiomatic postulate, for which, we exploit the appropriate Pfaffian form. The allowed adiabatic transformations are then obtained by solving the corresponding Cauchy problem, and are studied accordingly. Furthermore, we discuss the implications of our approach, regarding the the second and third laws of black hole thermodynamics. In particular, the merging of two extremal black holes is studied in detail.
Asymptotic symmetry of the Euclidean 3D gravity with torsion is described by two independent Virasoro algebras with different central charges. Elements of this boundary conformal structure are combined with Cardys formula to calculate the black hole entropy.
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