The gravitational perturbations of the Kerr black hole. II. The perturbations in the quantities which are finite in the stationary state

1978 ◽  
Vol 358 (1695) ◽  
pp. 441-465 ◽  
Keyword(s):  
Black Hole ◽  
Stationary State ◽  
Integrability Condition ◽  
Kerr Black Hole ◽  
Bianchi Identities ◽  
Radial Functions ◽  
Commutation Relations ◽  
Gravitational Perturbations ◽  
Relative Normalization

The present paper completes the integration of the linearized Newman-Penrose equations governing the gravitational perturbations of the Kerr black hole. The equations which determine the solutions are the four (complex) Bianchi identities (not used in part I) and the 24 equations which follow from the commutation relations. The principal results are (1) the demonstration that the perturbation in the Weyl Ψ 2 scalar must vanish in a gauge in which the scalars Ψ 1 and Ψ 3 are assumed to vanish identically; (2) the determination of the relative normalization of the radial functions (left unspecified in part I) through an integrability condition. Further, the solution to the integrability condition defines a function involving quadratures over Teukolsky’s radial and angular functions; and it is in terms of this function that the perturbations in the metric coefficients are determined.

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 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.

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.

On the equations governing the gravitational perturbations of the Kerr black hole

1976 ◽  
Vol 350 (1661) ◽  
pp. 165-174 ◽  
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Kerr Black Hole ◽  
Radial Equation ◽  
One Dimensional ◽  
Gravitational Perturbations ◽  
Dimensional Wave

Teukolsky’s radial equation governing the general, non-axisymmetric, gravitational perturbations of the Kerr black hole is reduced to the form of a one-dimensional wave equation by making use of the transformation which enables the treatment of the non-axisymmetric modes in exactly the same way as the axisymmetric modes.

scholarly journals INSTABILITIES IN KERR SPACETIMES

2011 ◽  
Vol 20 (supp01) ◽  
pp. 27-31 ◽  
Author(s):  
GUSTAVO DOTTI ◽  
REINALDO J. GLEISER ◽  
IGNACIO F. RANEA-SANDOVAL
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Infinite Family ◽  
Dirac Field ◽  
Cauchy Horizon ◽  
Kerr Spacetime ◽  
Gravitational Perturbations ◽  
Black Hole Interior ◽  
The Stability ◽  
Do So

We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions to the radial and angular Teukolsky's equations with different spin weights, particulary s = ±1 representing electromagnetic perturbations, s = ±1/2 representing a perturbation by a Dirac field and s = 0 representing perturbations by a scalar field. By analizing the properties of radial and angular eigenvalues we prove the existence of an infinite family of unstable modes.

scholarly journals Analytic solution of a magnetized tori with magnetic polarization around Kerr black holes

2018 ◽  
Vol 619 ◽  
pp. A57 ◽  
Author(s):  
Oscar M. Pimentel ◽  
Fabio D. Lora-Clavijo ◽  
Guillermo A. Gonzalez
Keyword(s):  
Black Hole ◽  
Magnetic Susceptibility ◽  
Integrability Condition ◽  
Kerr Black Hole ◽  
Hydrodynamic Pressure ◽  
Test Fluid ◽  
Magnetic Media ◽  
Magnetic Polarization ◽  
Fluid Approximation ◽  
Opposite Behavior

We present the first family of magnetically polarized equilibrium tori around a Kerr black hole. The models were obtained in the test fluid approximation by assuming that the tori is a linear media, making it is possible to characterize the magnetic polarization of the fluid through the magnetic susceptibility χm. The magnetohydrodynamic (MHD) structure of the models was solved by following the Komissarov approach, but with the aim of including the magnetic polarization of the fluid, the integrability condition for the magnetic counterpart was modified. We build two kinds of magnetized tori depending on whether the magnetic susceptibility is constant in space or not. In the models with constant χm, we find that the paramagnetic tori ( χm >  0) are more dense and less magnetized than the diamagnetic ones ( χm <  0) in the region between the inner edge, rin, and the center of the disk, rc; however, we find the opposite behavior for r >  rc. Now, in the models with non-constant χm, the tori become more magnetized than the Komissarov solution in the region where ∂χm/∂r <  0, and less magnetized when ∂χm/∂r >  0. Nevertheless, it is worth mentioning that in all solutions presented in this paper the magnetic pressure is greater than the hydrodynamic pressure. These new equilibrium tori can be useful for studying the accretion of a magnetic media onto a rotating black hole.

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