Hidden conformal symmetry of rotating black holes in the five-dimensional Gödel universe

Abstract

We have investigated the hidden conformal symmetry of generic nonextremal rotating black holes in the five-dimensional Gödel universe. In a range of parameters, the low-frequency massless scalar wave equation in the "near region" can be described by an SL(2, R) L × SL(2, R) R conformal symmetry. We further found that the microscopic entropy via Cardy formula matches the macroscopic Bekenstein-Hawking entropy and the absorption cross section for the massless scalar also agrees with the one for the two dimensional finite temperature conformal field theory (CFT). All these evidences support the conjecture that the generic non-extremal rotating black hole immersed in the Gödel universe can be dual to a two dimensional finite temperature CFT. In addition, we have reformulated the first laws of thermodynamics associated with the inner and outer horizons of the rotating Gödel-type black holes into the forms of conformal thermodynamics.

AdS SEGMENT AND HIDDEN CONFORMAL SYMMETRY IN GENERAL NONEXTREMAL BLACK HOLES

“…It implies that the general Kerr should be dual to a two-dimensioanl CFT with central charges c L = c R = 12J at temperatures (T L , T R ). The entropy of general Kerr black holes computed by using Cardy's formula agrees well with the BH area law for black hole entropy and the result appears to be valid for any values of M and J.More hidden conformal symmetries are found in various black hole spacetimes [9,10,11,12,13,14,15,16,17,18,19,20]. Recently, it is claimed in [21] that there is also an SL(2, R) symmetry in the wave equation in near regions of Schwarzschild black holes.…”

“…where Γ(θ) is the same as defined in Eq. (19) and ρ satisfies the condition (23) as well. This is more like a portion of warped AdS 3 space.…”

“…More hidden conformal symmetries are found in various black hole spacetimes [9,10,11,12,13,14,15,16,17,18,19,20]. Recently, it is claimed in [21] that there is also an SL(2, R) symmetry in the wave equation in near regions of Schwarzschild black holes.…”

Mass and angular momentum of charged rotating Gödel black holes in five-dimensional minimal supergravity

“…Besides, the Euler angles θ, φ and ψ range from 0 < θ < π, 0 < φ < 4π and 0 < ψ < 2π respectively. The solution (3.1) behaves asymptotically as the five-dimensional rotating Gödel-type universe, which provides an ideal platform to test the various traditional properties of gravity theories [49,50,51,52,53,54,55,56]. As a matter of fact, the metric (3.1) can cover several well-known solutions in the literature on the choices of appropriate parameters.…”