Yongjoon Kwon

Area spectra of the rotating BTZ black hole from quasinormal modes

Following Bekensteins suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the transition frequency of the black hole, analogous to the case of a hydrogen atom, in the semiclassical limit. According to Bohrs correspondence principle, this transition frequency at a large quantum number is equal to the classical oscillation frequency. For the corresponding classical system of periodic motion with this oscillation frequency, an action variable is identified and quantized via the Bohr–Sommerfeld quantization, from which the quantized spectrum of the horizon area is obtained. This method can be applied for black holes with discrete quasinormal modes. As an example, we apply the method for both non-rotating and rotating BTZ black holes and obtain that the spectrum of the horizon area is equally spaced and independent of the cosmological constant for both cases.

Quasi-normal modes for new type black holes in new massive gravity

We obtain the quasi-normal mode (QNM) frequencies of scalar perturbation on new type black holes in three-dimensional new massive gravity. In some special cases, the exact QNM frequencies are obtained by solving scalar field equations exactly. On some parameter regions, the highly damped QNM frequencies are obtained in an analytic form by the so-called Stokes line method. This study on QNMs sheds some light on the mysterious nature of these black holes. We also comment about the AdS/CFT correspondence and the entropy/area spectrum for new type black holes.

Entropy spectra of black holes from resonance modes in scattering by the black holes

Since Bekensteins proposal that a black hole has an equally spaced area spectrum, the quasinormal modes (QNM) as the characteristic modes of a black hole have been used for obtaining the horizon area spectrum of the black hole. However, the area spectrum of the Kerr black hole in some previous works was inconsistent with Bekensteins proposal. In this paper, noting that black holes can have three types of resonance modes which are QNM, total transmission modes (TTM), and total reflection modes (TRM), we propose that all of these modes in a highly damped regime should be used in quantizing the black hole. Although the QNM and the TTM of the Kerr black hole give us complicated quantization conditions from the Bohr–Sommerfeld quantization of an action variable, we find a very simple result from the TRM. It gives an equally spaced outer horizon area. Therefore, by the Bekenstein–Hawking area law, we find that the Kerr black hole has universal behavior of the equally spaced entropy spectrum. With the same argument, we find that the Reissner–Nordstrom black hole also has the equally spaced entropy spectrum.

Holographic renormalization and stress tensor in new massive gravity

A bstractWe obtain holographically renormalized boundary stress tensor with the em- phasis on a special point in the parameter space of three dimensional new massive gravity, using the so-called Fefferman-Graham coordinates with relevant counter terms. Through the linearized equations of motion with a standard prescription, we also obtain correlators among these stress tensors. We argue that the self-consistency of holographic renormaliza- tion determines counter terms up to unphysical ambiguities. Using this renormalized stress tensor in Fefferman-Graham coordinates, we obtain the central charges of dual CFT, and mass and angular momentum of some AdS black hole solutions. These results are consistent with the previous ones obtained by other methods. In this study on the Fefferman-Graham expansion of new massive gravity, some aspects of higher curvature gravity are revealed.

AdS/BCFT Correspondence for Higher Curvature Gravity: An Example

A bstractWe consider the effects of higher curvature terms on a holographic dual description of boundary conformal field theory. Specifically, we consider three-dimensional gravity with a specific combination of Ricci tensor square and curvature scalar square, so called, new massive gravity. We show that a boundary entropy and an entanglement entropy are given by similar expressions with those of the Einstein gravity case when we introduce an effective Newton’s constant and an effective cosmological constant. We also show that the holographic g-theorem still holds in this extension, and we give some comments about the central charge dependence of boundary entropy in the holographic construction. In the same way, we consider new type black holes and comment on the boundary profile. More-over, we reproduce these results through auxiliary field formalism in this specific higher curvature gravity.

Extremal black holes and holographic c-theorem

Abstract We found Bogomolʼnyi type of the first order differential equations in three-dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled. Using these equations in Einstein gravity, we obtain analytic solutions corresponding to extremally rotating hairy black holes. We also obtain perturbatively extremal black hole solutions in new massive gravity using these lower order differential equations. All these solutions have the anti-de Sitter spaces as their asymptotic geometries and as the near horizon ones. This feature of solutions interpolating two anti-de Sitter spaces leads to the construction of holographic c -theorem in these cases. Since our lower order equations reduce naturally to the well-known equations for domain walls, our results can be regarded as the natural extension of domain walls to more generic cases.

Some properties of the de Sitter black holes in three dimensional spacetime

A bstractWe investigate the physical properties of the de Sitter spacetime and new type-de Sitter black holes in new massive gravity, a higher derivative gravity theory in three dimensions. We calculate thermodynamic quantities and check that the first law of thermodynamics is satisfied. In particular, we obtain the energies of the de Sitter spacetime and new type-de Sitter black holes from the renormalized Brown-York boundary stress tensor on the Euclidean surfaces at late temporal infinity. We also obtain the quasinormal modes and by using them we find that the entropy spectra are equally spaced via semi-classical quantization.

On Quasinormal modes and Quantization of Area of Black Holes

Perturbations of black holes give very important tools of understanding physical properties of black holes. The relaxation of the perturbation is described by quasinormal modes with complex frequency. Using this, there has been some proposal of Hod and later by Maggiore that one can obtain quantization of the area of black holes. These ideas, when applied to rotating black holes were less than controversial. In this work we address how the are can be quantized with equal spacing. We also comment on application of this to other black holes in three dimensional spacetime.