Kerr Gravitational Field Research Articles

Circularly Polarized Light in Kerr Gravitational Field: Its Implication in Spin-Gravity Interaction

Circularly Polarized Light in Kerr Gravitational Field: Its Implication in Spin-Gravity Interaction

Equivalence and hermiticity of Dirac Hamiltonians in the Kerr gravitational field

In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac Hamiltonian and the self‐adjoint Hamiltonian with a flat scalar product of the wave functions are physically equivalent. Operators of transformation of Chandrasekhar's Hamiltonian and wave functions to the η representation with a flat scalar product are defined explicitly. If the domain of the wave functions of Dirac's equation in the Kerr field is bounded by two‐dimensional surfaces of revolution around the z axis, Chandrasekhar's Hamiltonian and the self‐adjoint Hamiltonian in the η representation are Hermitian with equality of the scalar products, . image

Wave and particle scattering properties of high-speed Kerr black holes

The light-like limit of the Kerr gravitational field relative to a distant observer moving rectilinearly in an arbitrary direction is an impulsive plane gravitational wave with a singular point on its wave front. By colliding particles with this wave we show that they have the same focusing properties as high-speed particles scattered by the original black hole. By colliding photons with the gravitational wave we show that there is a circular disc, centred on the singular point on the wave front, having the property that photons colliding with the wave within this disc are reflected back and travel with the wave. This result is approximate in the sense that there are observers who can see a dim (as opposed to opaque) circular disc on their sky. By colliding plane electromagnetic waves with the gravitational wave we show that the reflected electromagnetic waves are the high-frequency waves.

Scattering of high-speed particles in the Kerr gravitational field

We calculate the angles of deflection of high-speed particles projected in an arbitrary direction into the Kerr gravitational field. This is done by first calculating the lightlike boost of the Kerr gravitational field in an arbitrary direction and then using this boosted gravitational field as an approximation to the gravitational field experienced by a high-speed particle. In the rest frame of the Kerr source the angles of deflection experienced by the high-speed test particle can then easily be evaluated.

Lightlike boost of the Kerr gravitational field

We describe light-like boosts of the Kerr gravitational field transverse and parallel to the symmetry axis. In the transverse case the boosted field is that of an impulsive gravitational wave having a line singularity displaced relative to its position if the rotation of the source were removed. The parallel boost is insensitive to the rotation of the source. The literature contains a number of diverse results for light-like boosts of the Kerr gravitational field. Our conclusions confirm the correctness of the limits calculated by Balasin and Nachbagauer [Class.and Quantum Grav.13(1996),731]. To avoid any ambiguity our approach is centered on evaluating the light-like boost of the Riemann tensor for the Kerr space-time with the metric playing a secondary role.

Scattering ofscalar waves by rotating black holes

We study the scattering of massless scalar waves by a Kerr black hole byletting plane monochromatic waves impinge on the black hole. Wecalculate the relevant scattering phase-shifts using the Prüferphase-function method, which is computationally efficient and also reliablefor high frequencies and/or large values of the angular multipoleindices (l, m). We use the obtained phase-shifts and the partial-waveapproach to determine differential cross sections and deflectionfunctions. Results for off-axis scattering (waves incident alongdirections misaligned with the black hole's rotation axis) are obtained forthe first time. Inspection of the off-axis deflection functions reveals thesame scattering phenomena as in Schwarzschild scattering. In particular,the cross sections are dominated by the glory effect and the forward(Coulomb) divergence due to the long-range nature of the gravitationalfield. In the rotating case the overall diffraction pattern is`frame-dragged' and as a result the glory maximum is not observed in theexact backward direction. We discuss the physical reason for thisbehaviour, and explain it in terms of the distinction between prograde andretrograde motion in the Kerr gravitational field. Finally, we also discussthe possible influence of the so-called superradiance effect on thescattered waves.

Radiation reaction in the Kerr gravitational field

The radiative Green functions for the massless scalar, electromagnetic and gravitational perturbations of the Kerr space-time are constructed using the Teukolsky (1973) formalism. The reaction force acting upon a test particle, which can emit radiation of any spin s=0, 1, 2, is calculated and shown to account correctly for the energy and the angular momentum carried away by radiation to infinity and to the event horizon. The azimuthal component of the reaction force is found to remain finite for a particle at rest in the Boyer-Lindquist coordinates owing to non-zero angular momentum transfer to the rotating hole. This anomalous static force of radiation reaction emerges as the counteraction to Hawking's tidal friction.

Radiation from relativistic particles in nongeodesic motion in a strong gravitational field

The scalar and electromagnetic radiation emitted by relativistic particles moving along the stable nongeodesic trajectories in the Kerr gravitational field are described. Two particular models of the nongeodesic motion are developed involving a slightly charged rotating black hole and a rotating black hole immersed in an external magnetic field.

Relativistic fluid disks in orbit around Kerr black holes. II - Equilibrium structure of disks with constant angular momentum per baryon

view Abstract Citations (17) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Relativistic fluid disks in orbit around Kerr black holes. II. Equilibrium structure of disks with constant angular momentum per baryon. Fishbone, L. G. Abstract For the stationary, axisymmetric, purely azimuthal flow of isentropic fluid in an arbitrary stationary, axisymmetric gravitational field, we explore disk equilibrium configurations with the property that the fluid's angular momentum per baryon and angular-momentum-corrected injection energy per baryon are constant. Such two-parameter disks in a Kerr gravitational field can begin as near to the Kerr source as the radius of the marginally bound equatorial circular orbit. Given reasonable choices of their defining parameters, the disks are thick and are characterized by high fluid temperatures. Particles falling into them from afar lose little of their rest-mass energy. Subject headings: black holes - hydrodynamics - relativity Publication: The Astrophysical Journal Pub Date: July 1977 DOI: 10.1086/155361 Bibcode: 1977ApJ...215..323F Keywords: Angular Momentum; Black Holes (Astronomy); Disks (Shapes); Equilibrium Flow; Relativistic Effects; Astronomical Models; Baryons; Gravitational Effects; Astrophysics full text sources ADS |

Applications of Geometrical Optics to the Kerr Metric. 11. Numerical Results

view Abstract Citations (20) References (5) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Applications of Geometrical Optics to the Kerr Metric. 11. Numerical Results Pineault, Serge ; Roeder, R. C. Abstract Numerical integrations are performed to investigate the effects of a strong Kerr gravitational field on optical images. In addition to the well-known intensification due to gravitational focusing, the distortion and orientation of various images, and the rotation of the polarization plane, are obtained in terms of the source position. These effects are analyzed from the point of view of (a) a distant observer looking at a source in a close orbit around a Kerr black hole, and (b) a close observer looking at the distant universe. The rotation of the black hole is found to introduce interesting features which are absent in a spherical field. Subject headings: black holes - gravitation - polarization - relativity Publication: The Astrophysical Journal Pub Date: April 1977 DOI: 10.1086/155186 Bibcode: 1977ApJ...213..548P full text sources ADS |

Applications of Geometrical Optics to the Kerr Metric. Analytical Results

Numerical integrations are performed to investigate the effects of a strong Kerr gravitational field on optical images. In addition to the well-known intensification due to gravitational focusing, the distortion and orientation of various images, and the rotation of the polarization plane, are obtained in terms of the source position. These effects are analyzed from the point of view of (a) a distant observer looking at a source in a close orbit around a Kerr black hole, and (b) a close observer looking at the distant universe. The rotation of the black hole is found to introduce interesting features which are absent in a spherical field.

Quantization of a scalar field in the Kerr spacetime

The interaction of a scalar field with the Kerr gravitational field is studied. The properties of the Klein--Gordon equation in the Kerr metric are reviewed, and a two-component formalism is developed. This formalism expresses the one-particle quantum theory for a massive scalar particle in the Kerr metric. A semiclassical analysis of the spontaneous emission of particles by a Kerr black hole is given. The quantization of a scalar field in the Kerr metric is developed, and a treatment of the spontaneous particle creation is given. The particular quantization given here leads to emission only into the classical superradiant modes and hence no emission by a Schwarzschild black hole. In the case in which $omega$M is very much less than 1, where M is the mass of the black hole and $omega$ is the frequency of a given mode, an explicit expression may be given for the rate at which particles are emitted into each mode. In the case in which the particle's mass is zero and a is very much less than M, a = angular momentum per unit mass of the black hole, the total rate of loss of energy of the black hole is shown to be proportionalmore » to a$sup 6$/M$sup 8$. A discussion of the problem of the vacuum energy is given. It is shown that the energy of the vacuum state of a scalar field in a Kerr spacetime a very-much-less-than M is the same as that for a Schwarzschild (a = 0) spacetime. (AIP)« less

Electromagnetic radiation emitted by a particle in Kerr and Schwarzchild fields

A detailed analysis is made of the properties of electromagnetic radiation emitted by a charged particle in a circular geodesic orbit in the equatorial plane of a Kerr gravitational field. Equations are obtained to describe the spectral-angular, angular, and spectral distributions of the resulting radiation. The cases of nonrelativistic and relativistic velocities of the emitting charge are investigated. The enhancement of radiation from a charge due to a rotating black hole is considered. For certain values of the parameters the results obtained are applicable to the description of radiation emitted by a charge in a Schwarzchild field.

Solution of the Scalar Wave Equation in a Kerr Background by Separation of Variables

The effect of the Kerr gravitational field on wave phenomena is explored by examining the inhomogeneous wave equation for a scalar massive field in a Kerr background geometry. The equation is separated in Boyer-Lindquist coordinates. The angular functions are spheroidal harmonics, and the radial equation is reduced to a one-dimensional Schr\odinger equation with an effective potential.