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. 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.

scholarly journals Optical properties of Kerr–Newman spacetime in the presence of plasma

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Gulmina Zaman Babar ◽  
Abdullah Zaman Babar ◽  
Farruh Atamurotov
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Field Approximation ◽  
Weak Field ◽  
Jacobi Method ◽  
Plasma Parameters ◽  
Spin Parameter ◽  
Newman Black Hole ◽  
Shadow Cast ◽  
Thermal Radiations

Abstract We have studied the null geodesics in the background of the Kerr–Newman black hole veiled by a plasma medium using the Hamilton–Jacobi method. The influence of black hole’s charge and plasma parameters on the effective potential and the generic photon orbits has been investigated. Furthermore, our discussion embodies the effects of black hole’s charge, plasma and the inclination angle on the shadow cast by the gravity with and without the spin parameter. We examined the energy released from the black hole as a result of the thermal radiations, which exclusively depends on the size of the shadow. The angle of deflection of the massless particles is also explored considering a weak-field approximation. We present our results in juxtaposition to the analogous black holes in General Relativity, particularly the Schwarzschild and Kerr black hole.

scholarly journals AREA SPECTRUM OF KERR AND EXTREMAL KERR BLACK HOLES FROM QUASINORMAL MODES

2005 ◽  
Vol 20 (25) ◽  
pp. 1923-1932 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
ELIAS C. VAGENAS
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quasinormal Modes ◽  
Kerr Black Hole ◽  
Area Spectrum ◽  
The Real ◽  
Hole Area ◽  
Newman Black Hole ◽  
Discrete Area ◽  
Kerr Black Holes

Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form mΩ where Ω is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly spaced. Thus, we infer that the function describing the real part of quasinormal frequencies of Kerr black hole is not the correct one. This conclusion is in agreement with the numerical results for the highly damped quasinormal modes of Kerr black hole recently presented by Berti, Cardoso and Yoshida. On the contrary, extremal Kerr black hole is shown to have a discrete area spectrum which in addition is evenly spaced. The area spacing derived in our analysis for the extremal Kerr black hole area spectrum is not proportional to ln 3. Therefore, it does not give support to Hod's statement that the area spectrum [Formula: see text] should be valid for a generic Kerr–Newman black hole.

scholarly journals SEMICLASSICAL (QFT) AND QUANTUM (STRING) ROTATING BLACK HOLES AND THEIR EVAPORATION: NEW RESULTS

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1627-1648 ◽  
Author(s):  
A. BOUCHAREB ◽  
M. RAMÓN MEDRANO ◽  
N. G. SÁNCHEZ
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Angular Momentum ◽  
Emission Cross Section ◽  
Kerr Black Hole ◽  
Hawking Temperature ◽  
Extremal Black Hole ◽  
Entropy Formula ◽  
Newman Black Hole ◽  
String State

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr–Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross-section of strings by a Kerr–Newman black hole (KNbh). It shows the black hole emission at the Hawking temperature T sem in the early stage of evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature Ts at the last stages. New bounds on J and Q emerge in the quantum string regime (besides the known ones of the classical/semiclassical QFT regime). The last state of evaporation of a semiclassical Kerr–Newman black hole with mass M > m Pl , angular momentum J and charge Q is a string state of temperature Ts, string mass Ms, J = 0 and Q = 0, decaying as usual quantum strings do into all kinds of particles. (Naturally, in this framework, there is no loss of information, (there is no paradox at all).) We compute the string entropy Ss(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at Ts) we find for high j (extremal string states j → m2α′c), a new phase transition at a temperature [Formula: see text], higher than Ts. By precisely identifying the semiclassical and quantum (string) gravity regimes, we find a new formula for the Kerr black hole entropy S sem (M, J), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For M ≫ m Pl and J < GM2/c, [Formula: see text] is the leading term, but for high angular momentum, (nearly extremal case J = GM2/c), a gravitational phase transition operates and the whole entropy S sem is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. This new extremal black hole transition occurs at a temperature T sem J = (J/ℏ)T sem , higher than the Hawking temperature T sem .

scholarly journals Introduction to the Views of Distant Objects in Kerr - Newman Spacetimes

1996 ◽  
Vol 49 (3) ◽  
pp. 623
Author(s):  
William E Metzenthen
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Gravitational Effects ◽  
Visual Appearance ◽  
Newman Black Hole

Gravitational effects cause the visual appearance of the external universe to be distorted to observers near a Kerr–Newman black hole. This paper introduces the problem and presents some computer-generated pictures which show how the 'sky' appears to an observer near a Kerr black hole.

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
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