Horizon Of BTZ Black Hole Research Articles

A simple quantum test for smooth horizons

We develop a new test that provides a necessary condition for a quantum state to be smooth in the vicinity of a null surface: “near-horizon modes” that can be defined locally near any patch of the null surface must be correctly entangled with each other and with their counterparts across the surface. This test is considerably simpler to implement than a full computation of the renormalized stress-energy tensor. We apply this test to Reissner-Nordström black holes in asymptotically anti-de Sitter space and provide numerical evidence that the inner horizon of such black holes is singular in the Hartle-Hawking state. We then consider BTZ black holes, where we show that our criterion for smoothness is satisfied as one approaches the inner horizon from outside. This results from a remarkable conspiracy between the properties of mode-functions outside the outer horizon and between the inner and outer horizon. Moreover, we consider the extension of spacetime across the inner horizon of BTZ black holes and show that it is possible to define modes behind the inner horizon that are correctly entangled with modes in front of the inner horizon. Although this provides additional suggestions for the failure of strong cosmic censorship, we lay out several puzzles that must be resolved before concluding that the inner horizon will be traversable.

Structure constants from modularity in warped CFT

We derive a universal formula for the asymptotic growth of the mean value of three-point coefficient for Warped Conformal Field Theories (WCFTs), and provide a holographic calculation in BTZ black holes. WCFTs are two dimensional quantum field theories featuring a chiral Virasoro and U(1) Kac-Moody algebra, and are conjectured to be holographically dual to quantum gravity on asymptotically AdS3 spacetime with Compère- Song-Strominger boundary conditions. The WCFT calculation amounts to the calculation of one-point functions on torus, whose high temperature limit can be approximated by using modular covariance of WCFT, similar to the derivation of Cardy formula. The bulk process is given by a tadpole diagram, with a massive spinning particle propagates from the infinity to the horizon, and splits into particle and antiparticle which annihilate after going around the horizon of BTZ black holes. The agreement between the bulk and WCFT calculations indicates that the black hole geometries in asymptotically AdS3 spacetimes can emerge upon coarse-graining over microstates in WCFTs, similar to the results of Kraus and Maloney in the context of AdS/CFT [1].

Compact chiral boson fields on the horizon of BTZ black hole

In the previous work, it was shown that the degrees of freedom on the horizon of BTZ black hole can be described by two chiral massless scalar fields with opposite chirality. In this paper, we continuous this research. It is found that the scalar field is actually a compact boson field on a circle. The compactness results in the quantization of the black hole radius. Then we quantize the two boson fields and get two abelian Kac-Moody algebras. From the boson field, one can construct the full W1+∞ algebra which was used to classify the BTZ black holes.

Aspects of flat/CCFT correspondence

Flat/contracted conformal field theory (CCFT) is a correspondence between gravity in asymptotically flat backgrounds and a field theory which is given by contraction of conformal field theory. In order to find a dictionary for flat/CCFT correspondence one can start from the AdS/CFT and take the contraction of CFT in the boundary as the dual description of the flat-space limit (zero cosmological constant limit) of the asymptotically AdS spacetimes in the bulk side. In this paper we show that the Cardy-like formula of CCFT2 is given by contraction of a proper formula in the CFT2. This formula is the modified Cardy formula which gives the entropy of inner horizon of BTZ black holes.

Dirac particles tunneling from BTZ black hole

We calculated the Dirac particles' Hawking radiation from the outer horizon of BTZ black hole via tunneling formalism. Applying WKB approximation to the Dirac equation in (2+1)-dimensional BTZ spacetime background, we obtain the radiation spectrum for fermions and Hawking temperature of BTZ black hole. The results obtained by taking the fermion tunneling into account are consistent with the previous literatures.

Thermodynamic Interpretation of Field Equations at Horizon ofBTZ Black Hole

A spacetime horizon comprising with a black hole singularity acts like aboundary of a thermal system associated with the notions of temperatureand entropy. In the case of static metric ofBanados–Teitelboim–Zanelli (BTZ) black hole, the field equations near the horizon boundary can be expressed as a thermal identity dE = TdS+PrdA, where E = M is the mass of BTZ black hole, dA is thechange in the area of the black hole horizon when the horizon isdisplaced infinitesimally small, Pr is the radial pressure providedby the source of Einstein equations, S = 4πa is the entropy and T = κ/2π is the Hawking temperature associated with the horizon.This approach is studied further to generalize it for non-static BTZblack hole, showing that it is also possible to interpret thefield equation near horizon as a thermodynamic identity dE = TdS+PrdA+Ω+dJ, where Ω+ is the angularvelocity and J is the angular momentum of BTZ black hole. Theseresults indicate that the field equations for BTZ black holepossess intrinsic thermodynamic properties near the horizon.