Sang-Heon Yi

Quasilocal conserved charges in the presence of a gravitational Chern-Simons term

We extend our recent work on the quasilocal formulation of conserved charges to a theory of gravity containing a gravitational Chern-Simons term. As an application of our formulation, we compute the off-shell potential and quasilocal conserved charges of some black holes in three-dimensional topologically massive gravity. Our formulation for conserved charges reproduces very effectively the well-known expressions on conserved charges and the entropy expression of black holes in the topologically massive gravity.

Hawking-Page phase transition in BTZ black hole revisited

A bstractWe consider the Hawking-Page phase transition between the BTZ black hole of M ≥ 0 and the thermal soliton of M = −1. In this system, there exists a mass gap so that there does not seem to exist a continuous thermodynamic phase transition. We consistently construct the off-shell free energies of the black hole and the soliton by properly taking into account the conical space. And then, the continuous off-shell free energy to describe tunneling effect can be realized through non-equilibrium solitons.We derive the BPS type of first order differential equations for the rotating black hole solutions in the three-dimensional Einstein gravity coupled minimally with a self-interacting scalar field, using fake supersymmetry formalism. It turns out that the formalism is not complete and should be augmented by an additional equation to imply the full equations of motion. We identify this additional equation as a constraint by using an effective action method. By computing the renormalized boundary stress tensor, we obtain the mass and angular momentum of the black hole solutions of these first order equations and confirm that they saturate the BPS bound.

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.

Noncritical Einstein-Weyl gravity and the AdS/CFT correspondence

A bstractWe explore four-dimensional Einstein-Weyl gravity and supergravity on anti-de Sitter spacetime. For a specific range of the coupling with appropriate boundary conditions, we show the effective equivalence of the theory with Einstein gravity and AdS supergravity at the quadratic Lagrangian level. Furthermore we show that these equivalences can be promoted to the full nonlinear level. We also show that the similar behavior holds for the generalized Gibbons-Hawking terms. From this we find that the correlation functions in the dual conformal field theory of Einstein-Weyl gravity and supergravity can be readily read off from corresponding ones from Einstein gravity and AdS supergravity. We also give comments on some issues in critical gravity and supergravity as well as conformal gravity and supergravity.

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.

Conserved quantities and Virasoro algebra in new massive gravity

A bstractUsing the off-shell Noether current and potential we compute the entropy for the AdS black holes in new massive gravity. For the non-extremal BTZ black holes by implementing the so-called stretched horizon approach we reproduce the correct expression for the horizon entropy. For the extremal case, we adopt standard formalism in the AdS/CFT correspondence and reproduce the corresponding entropy by computing the central extension term on the asymptotic boundary of the near horizon geometry. We explicitly show the invariance of the angular momentum along the radial direction for extremal as well as non-extremal BTZ black holes in our model. Furthermore, we extend this invariance for the black holes in new massive gravity coupled with a scalar field, which correspond to the holographic renormalization group flow trajectory of the dual field theory. This provides another realization for the holographic c-theorem.

On classical equivalence between noncritical and Einstein gravity: the AdS/CFT perspectives

A bstractWe find that noncritical gravity, a special class of higher derivative gravity, is classically equivalent to Einstein gravity at the full nonlinear level. We obtain the viscosity-to-entropy ratio and the second order transport coefficients of the dual fluid of noncritical gravity to all orders in the coupling of higher derivative terms. We also compute the holographic entanglement entropy in the dual CFT of noncritical gravity. All these results confirm the nonlinear equivalence between noncritical gravity and Einstein gravity at the classical level.

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.

Born-Infeld Type Extension of (Non-)Critical Gravity

We consider the Born-Infeld-type extension of (non-)critical gravity which is higher curvature gravity on anti-de Sitter space with specific combinations of scalar curvature and Ricci tensor. This theory may also be viewed as a natural extension of three-dimensional Born-Infeld new massive gravity to arbitrary dimensions. We show that this extension is consistent with the holographic