The Kerr/CFT correspondence

Abstract

Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J = GM 2 ) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c L = 12J . This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T L = 1 2π and conjugate energy given by the zero mode generator, L 0 , of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S micro = 2πJ for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S macro = Area 4 G . The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c L = 12J , and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c L ∼ 2 × 10 79 . ‡On leave from the Institute

The Brown-York mass of black holes in Warped Anti-de Sitter space

“…This represents one of the most appealing attempts to generalize holography to non-AdS spaces, and this is because WAdS spaces appear in several contexts. For instance, WAdS spaces provide gravity duals for condensed matter systems with Schrödinger symmetry [12,13], they are closely related to the geometry of rotating black holes [14,15], and they also appear in relation to many other interesting subjects [16][17][18]. Asymptotically WAdS 3 spaces turn out to be exact solutions of String Theory [19][20][21][22][23] as well as of other models of threedimensional gravity, including Higher-Spin Gravity [24], Topologically Massive Gravity (TMG) [25,26], and New Massive Gravity (NMG) [27].…”

Acoustic black holes and universal aspects of area products

“…Thus, we have found an equivalence that has a very high resemblance with a correspondence between microscopic description of gravitational black holes entropy in five/four dimensions and two-dimensional conformal field theory [21] (one of the first clues of the gauge/gravity duality, holography or Maldacena's correspondence [23]) -see also the recent fluid/gravity duality [26]. Particularly, our system seems to develop an analogue of the Kerr/CFT correspondence established in [22]. Although we have not addressed more properties to support (or proof) this equivalence, we find that we have presented strong enough evidences.…”

“…As was shown in [22], even though extreme Kerr has zero Hawking temperature, the quantum fields outside the horizon are not in a pure state. Plugging this temperature and the central charge into Eq.…”

“…This observation has a very high resemblance with the microscopic description of the entropy of four and five-dimensional gravitational black holes in terms of string theory which can be understood as a (1+1) -dimensional conformal field theory [21]. In order to support this equivalence, let us now focus on the Kerr/CFT correspondence [22]. In this correspondence it is shown that quantum gravity on NHEK (near-horizon extreme Kerr) is holographically dual to a 2d conformal field theory with central charge c L = 12J.…”

“…Since the black hole entanglement entropy is given in terms of the outer horizon area S BH ∼ A + ≥ A + A − , then as we shall see later, this relation between equations (1) and (2) suggests the area products for acoustic black holes should be quantized as in most of gravitational systems [20]. Furthermore, in the latter case it is already well known that the microscopic description of the entropy of four and five-dimensional gravitational black holes can be computed in terms of string theory which can be understood as a (1+1) -dimensional conformal field theory [21] -see also Kerr/CFT correspondence [22]. As we shall see, in our present study we have found an equivalence that has a very high resemblance with this gravitational duality (one of the first clues of gauge/gravity duality, holography or Maldacena's correspondence [23]).…”