scholarly journals Breaking away from the near horizon of extreme Kerr

2020 ◽  
Vol 8 (6) ◽  
Author(s):  
Alejandra Castro ◽  
Victor Godet
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Conformal Symmetry ◽  
Kerr Black Hole ◽  
Einstein Equations ◽  
The Other ◽  
Conformal Dimension ◽  
Gravitational Perturbations ◽  
Horizon Geometry ◽  
Metric Fluctuations

We study gravitational perturbations around the near horizon geometry of the (near) extreme Kerr black hole. By considering a consistent truncation for the metric fluctuations, we obtain a solution to the linearized Einstein equations. The dynamics is governed by two master fields which, in the context of the nAdS_22/nCFT_11 correspondence, are both irrelevant operators of conformal dimension \Delta=2Δ=2. These fields control the departure from extremality by breaking the conformal symmetry of the near horizon region. One of the master fields is tied to large diffeomorphisms of the near horizon, with its equations of motion compatible with a Schwarzian effective action. The other field is essential for a consistent description of the geometry away from the horizon.

scholarly journals Notes on the hidden conformal symmetry in the near horizon geometry of the Kerr black hole

2011 ◽  
Vol 844 (1) ◽  
pp. 146-163 ◽  
Author(s):  
Yoshinori Matsuo ◽  
Takuya Tsukioka ◽  
Chul-Moon Yoo
Keyword(s):  
Black Hole ◽  
Conformal Symmetry ◽  
Kerr Black Hole ◽  
Horizon Geometry

scholarly journals Hidden conformal symmetry of the Kerr black hole

2010 ◽  
Vol 82 (2) ◽  
Author(s):  
Alejandra Castro ◽  
Alexander Maloney ◽  
Andrew Strominger
Keyword(s):  
Black Hole ◽  
Conformal Symmetry ◽  
Kerr Black Hole

The gravitational perturbations of the Kerr black hole I. The perturbations in the quantities which vanish in the stationary state

1978 ◽  
Vol 358 (1695) ◽  
pp. 421-439 ◽  
Keyword(s):  
Black Hole ◽  
Stationary State ◽  
Weyl Tensor ◽  
Kerr Black Hole ◽  
Maxwell Field ◽  
Subsequent Work ◽  
Kerr Geometry ◽  
Gravitational Perturbations ◽  
Newman Black Hole ◽  
Basic Equations

As a preliminary towards a complete integration of the Newman-Penrose equations governing the gravitational perturbations of the Kerr black hole, the perturbations in the spin coefficients and in the components of the Weyl tensor, which vanish in the stationary state, are considered. The manner of treatment of the basic equations yields Teukolsky’s equations expressed directly in terms of the basic derivative operators of the theory and, further, suggests a preferred gauge in which two of the components of the Weyl tensor are governed by the same equations as a Maxwell field. Various identities and relations that are needed in subsequent work are assembled. In two appendixes, the solution of Maxwell’s equations in Kerr geometry and the perturbations of the charged Kerr-Newman black hole are considered.

scholarly journals A NOTE ON KERR/CFT AND FREE FIELDS

2010 ◽  
Vol 25 (20) ◽  
pp. 3965-3973 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Black Hole ◽  
Boundary Conditions ◽  
Isometry Group ◽  
Free Field ◽  
Kerr Black Hole ◽  
Virasoro Algebra ◽  
Free Fields ◽  
Horizon Geometry

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL (2, ℝ) × U (1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.

scholarly journals GRAVITATIONAL PERTURBATIONS OF THE KERR BLACK HOLE DUE TO ARBITRARY SOURCES

2002 ◽  
Vol 11 (08) ◽  
pp. 1331-1346 ◽  
Author(s):  
CLAUDIA MORENO ◽  
DARÍO NÚÑEZ
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Weyl Tensor ◽  
Kerr Black Hole ◽  
Null Vector ◽  
Source Terms ◽  
Field Equations ◽  
Null Tetrad ◽  
Gravitational Perturbations

We describe the Kerr black hole in the ingoing and outgoing Kerr–Schild horizon penetrating coordinates. Starting from the null vector naturally defined in these coordinates, we construct the null tetrad for each case, as well as the corresponding geometrical quantities allowing us to explicitly derive the field equations for the perturbed scalar projections Ψ0(1) and Ψ4(1) of the Weyl tensor, including arbitrary source terms. This perturbative description, including arbitrary sources, described in horizon penetrating coordinates is desirable in several lines of research on black holes, and contributes to the implementation of a formalism aimed to study the evolution of the spacetime in the region where two black holes are close together.

scholarly journals A NEAR-NHEK/CFT CORRESPONDENCE

2010 ◽  
Vol 25 (30) ◽  
pp. 5517-5527 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Angular Momentum ◽  
Isometry Group ◽  
Kerr Black Hole ◽  
Two Dimensional ◽  
Conformal Field ◽  
Horizon Geometry ◽  
Cardy Formula ◽  
Asymptotic Symmetries

We consider excitations around the recently introduced near-NHEK metric describing the near-horizon geometry of the near-extremal four-dimensional Kerr black hole. This geometry has a U (1)L × U (1)R isometry group which can be enhanced to a pair of commuting Virasoro algebras. We present boundary conditions for which the conserved charges of the corresponding asymptotic symmetries are well defined and nonvanishing and find the central charges cL = 12J/ℏ and cR = 0 where J is the angular momentum of the black hole. Applying the Cardy formula reproduces the Bekenstein–Hawking entropy of the black hole. This suggests that the near-extremal Kerr black hole is holographically dual to a nonchiral two-dimensional conformal field theory.

The gravitational perturbations of the Kerr black hole IV. The completion of the solutiont

1980 ◽  
Vol 372 (1751) ◽  
pp. 475-484 ◽  
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Space Time ◽  
Gravitational Perturbations ◽  
Kerr Space ◽  
The One

This paper eliminates the last remaining lacuna in the information that was needed to make the solution for the perturbations in the metric coefficients of the Kerr space-time fully explicit. The requisite information is obtained from a pair of equations which is complementary to the one considered in paper III; and the solution of the Newman-Penrose equations governing the perturbations is, thus, completed.

Quantization of electromagnetic and gravitational perturbations of a Kerr black hole

1981 ◽  
Vol 24 (2) ◽  
pp. 297-304 ◽  
Author(s):  
P. Candelas ◽  
P. Chrzanowski ◽  
K. W. Howard
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Gravitational Perturbations

scholarly journals Gravitational perturbations from NHEK to Kerr

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Alejandra Castro ◽  
Victor Godet ◽  
Joan Simón ◽  
Wei Song ◽  
Boyang Yu
Keyword(s):  
Black Hole ◽  
Line Element ◽  
Kerr Black Hole ◽  
Kerr Solution ◽  
Regularity Conditions ◽  
New Developments ◽  
Gravitational Perturbations ◽  
Dynamical Properties ◽  
Complete Characterisation

Abstract We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS2 holography.

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