Warped symmetries of the Kerr black hole

Abstract

We propose a set of diffeomorphism that act non-trivially near the horizon of the Kerr black hole.We follow the recent developments of Haco-Hawking-Perry-Strominger to quantify this phase space, with the most substantial difference being our choice of vectors fields. Our gravitational charges are organized into a Virasoro-Kac-Moody algebra with non-trivial central extensions. We interpret this algebra as arising from a warped conformal field theory. Using the data we can infer from this warped CFT description, we capture the thermodynamic properties of the Kerr black hole.

TsT, $$ \mathrm{T}\overline{\mathrm{T}} $$ and black strings

“…(3.13). This can be achieved by rescaling the coordinates and temperatures such that 16) while, at the same time, rescaling the size of the spatial circle ϕ ∼ ϕ+2π √ λ. Alternatively, these equations imply that backgrounds with different values of λ can be interpreted as describing the same solutions with rescaled spatial circles (3.15).…”

“…It is clear that most black holes including the real-world ones are not asymptotically AdS nor exhibit an AdS 3 factor in their near-horizon geometry, so AdS/CFT cannot be used as such. Various angles of attack to deal with more general black holes have been taken in recent years involving non-AdS geometries in the near-horizon region with both conformal [7][8][9] and non-conformal symmetries [10][11][12][13][14][15][16][17]. Although it has been suggested that conformal symmetry could play a role in understanding generic black holes, certain non-conformal symmetries have been able to account for the microscopic entropy of the corresponding solutions [13,14,[18][19][20][21] in the spirit of [3].…”

Modular Hamiltonians in flat holography and (W)AdS/WCFT

“…We refer to this class of holographic models as (W)AdS 3 /WCFT. Recent developments in (W)AdS 3 /WCFT include reproducing the Bekenstein-Hawking entropy of black holes from an analog of the Cardy formula in WCFT [24], average OPE coefficients of heavy-heavy-light correlators [76], bulk and boundary studies of entanglement entropy [25,30,35,54,77,78], one-loop partition functions [79], correlation functions [80], the modular bootstrap [81], quantum chaos [33], Rényi mutual information [82], bulk reconstruction [83], complexity [84], connections to complex SYK models [85,86], as well as the emergence of warped conformal symmetries in non-extremal Kerr black holes [87].…”

“…Since the swing surface γ A is homologous to the boundary interval A, Stoke's theorem guarantees that the gravitational charges evaluated on γ A and A agree with one another. In particular, for constant fluctuations of the zero-modes where δL(u) = δT 2 u and δJ(u) = 0 we have 87) where in the last equality we have used the holographic dictionary (4.66) and the expression for the holographic entanglement entropy (4.37). This provides an explicit check for the assumption (2.23) which states that the entanglement entropy can be calculated using the gravitational charge associated with the bulk modular flow generator ξ evaluated on the swing surface γ A .…”

Supersymmetric warped conformal field theory

“…This AdS 3 =WCFT correspondence has been studied in [14,16,[20][21][22][23][24]. Moreover, WCFT 2 could also appear in the WAdS 3 =WCFT 2 correspondence [25][26][27][28], in which the bulk gravity is a threedimensional topological massive gravity.…”