Lectures on the Kerr/CFT Correspondence

430

745

ABSTRACT. The surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed. They realize the symmetry algebra in general only up to a field-dependent central extension that satisfies a suitably generalized cocycle condition. This extension vanishes when using the globally well defined BMS algebra. For the Kerr black hole and the enlarged BMS algebra with both supertranslations and superrotations, some of the supertranslations charges diverge whereas there are no divergences for the superrotation charges. The central extension is proportional to the rotation parameter and involves divergent integrals on the sphere.

Section: Introductionmentioning

confidence: 99%

BMS charge algebra

Barnich

Troessaert

2011

430

745

“…Furthermore, the Kerr/CFT correspondence was developed even for generic non-extremal case. In a remarkable paper [14] it was argued that the existence of conformal invariance in a near horizon geometry is not a necessary condition, instead the existence of a local conformal invariance in the solution space 1 See the nice review [2] for complete references.…”

Section: Introductionmentioning

confidence: 99%

General hidden conformal symmetry of 4D Kerr-Newman and 5D Kerr black holes

Chen

Zhang

2011

There are two known CFT duals, namely the J-picture and the Q-picture, for a fourdimensional Kerr-Newman black hole, corresponding to the angular momentum J and the electric charge Q respectively. In our recent study we found a set of novel CFT duals for extremal Kerr-Newman black hole, incorporating these two pictures. The novel CFT duals are generated by the modular group SL(2, Z). In this paper we study these novel CFT duals for the generic non-extremal Kerr-Newman black hole. We investigate the hidden conformal symmetry in the low frequency scattering off Kerr-Newman black hole, from which the dual temperatures could be read. We find that there still exists a hidden conformal symmetry for a general CFT dual. We reproduce the correct BekensteinHawking entropy from the Cardy formula, assuming the form of the central charge being invariant. Moreover we compute the retarded Green's function in the general CFT dual picture and find it is in good match with the CFT prediction. Furthermore we discuss the hidden conformal symmetries of the five dimensional Kerr black hole and obtain the similar evidence to support the general dual CFT pictures. *

“…On the one hand, the BekensteinHawking entropy S BH = Area/4G N captures to leading order in 1/G N the UV density of states of a quantum gravity theory governed by the Einstein action in the IR. On the other hand, it is a reasonable expectation that, beyond its mere existence, the specific details of a UV-complete gravity theory are actually not needed to understand the area law, much like the actual quantum theory of atoms was not needed to derive the universal laws of thermodynamics for gases from statistical reasoning [25].…”

Section: Jhep06(2016)014mentioning

confidence: 99%

“…This includes for instance dS/CFT [41], AdS/Condensed Matter Theory [42,43], Non-relativistic Schrödinger and Lifshitz Holography [44], Hyperscaling geometries [45], Flat Space Holography [46] and Kerr/CFT [25,47] (references are by no means meant to be extensive, and point most of the time at reviews on the subjects).…”

Section: Jhep06(2016)014mentioning

confidence: 99%

Warped AdS3 black holes in higher derivative gravity theories

Detournay¹,

Douxchamps²,

Ng³

et al. 2016

We consider warped AdS 3 black holes in generic higher derivatives gravity theories in 2+1 dimensions. The asymptotic symmetry group of the phase space containing these black holes is the semi-direct product of a centrally extended Virasoro algebra and an affine u(1) Kac-Moody algebra. Previous works have shown that in some specific theories, the entropy of these black holes agrees with a Cardy-like entropy formula derived for warped conformal field theories. In this paper, we show that this entropy matching continues to hold for the most general higher derivative theories of gravity. We also discuss the existence of phase transitions.