Electromagnetic perturbations of charged Kerr geometry

The freedom associated with infinitesimal co-ordinate transformations and infinitesimal tetrad rotations within the Newman Penrose formalism is used when considering electromagnetic perturbations of type D geometries. In particular, it is shown that for the charged Kerr geometry, a suitable choice of tetrad rotation leads to equations for the perturbed Newman Penrose components ₀ and ₂ which are closely related to those for the uncharged case.     

New nonlinear intensity Kerr effect in the polar geometry

The problem of the electromagnetic wave reflection on the second optical harmonic from a semi-infinite optically isotropic magnetic medium is considered for the uniform magnetization direction corresponding to the polar Kerr effect. In the first approximation in magnetization, the method of Green’s tensor functions is used to derive expressions for the complex amplitudes of the wave fields for the incidence of s-and p-polarized waves (as well as of their superposition) on the medium. It is shown that, in the latter case, the nonlinear polar Kerr effect is of the intensity type. The dependences of the intensity effect on the angle of incidence of the inducing wave and on the angle of its polarization, which were obtained in numerical experiments, are presented. A comparative analysis of the linear and nonlinear intensity Kerr effects is carried out.     

Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry

The reflection of an electromagnetic wave at the second-harmonic frequency from a semi-infinite optically isotropic magnetic medium for the directions of uniform magnetization corresponding to the meridional and equatorial Kerr effects is considered. Using the Green’s tensor function technique, in the first approximation in magnetization, the expressions for complex amplitudes of the field are obtained for the s and p polarizations of the incident beam and their superpositions. It is shown that in the latter case, the meridional effect becomes intensity-related. Dependences of the intensity-related meridional and equatorial Kerr effects on the angle characterizing polarization of the pump wave are obtained by numerical calculations. A comparative analysis of the linear and nonlinear Kerr effects is made.     

Temperature and thermodynamic geometry of the Kerr-Sen black hole

This paper studies the thermodynamic properties of the Kerr-Sen black hole from the viewpoint of geometry.It calculates the temperature and heat capacity of the black hole,Weinhold metric and Ruppeiner metric are also obtained respectively.It finds that they are both curved and the curvature scalar of Weinhold curvature implies no information about the phase transition while the Ruppeiner one does.But they both carry no information about the second-order phase transition point reproduced from the capacity.Besides,the Legendre invariant metric of the Kerr-Sen black hole has been discussed and its scalar curvature gives the information about the second-order phase transition point.     

A newtonian model of the source of the Kerr metric

A complete newtonian model of the source of the gravitational field whose equipotential surfaces are confocal revolution ellipsoids is presented. The solution exhibits a singularity familiar from the Kerr metric.     

An approximation scheme for scalar waves in a Kerr geometry

An approximation scheme, analogous to ones previously considered for the Schwarzschild and Reissner-Nordström geometries, is applied to scalar waves in a Kerr geometry. Spectral curves of transmission coefficient for monochromatic, axially symmetric scalar waves imploding on a rotating black hole are calculated using the approximation scheme.Research supported in part by the Natural Sciences and Engineering Council of Canada.     

Charged particle motion in an electromagnetic field on Kerr background geometry

In this paper we study the trajectories of charged particles in an electromagnetic field superimposed on the Kerr background. The electromagnetic fields considered are of two types: (i) a dipole magnetic field with an associated quadrupole electric field, (ii) a uniform magnetic field. The contribution of the background geometry to the electromagnetic field is taken through the solutions of Petterson and Wald respectively. The effective potential is studied in detail for ther-motion of the particles in the equatorial plane and the orbits are obtained. The most interesting aspect of the study is the illustration of the effect of inertial frame dragging due to the rotation of the central star. This appears through the existence of nongyrating bound orbits at and inside the ergo surface. The presence of the magnetic field seems to increase the range of stable orbits, as was found in a previous study involving the Schwarzschild background.     

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

Toward the Kerr/CFT correspondence for the generic non-extremal Kerr black hole, the analysis of scattering amplitudes by near extremal Kerr provides a clue. This pursuit reveals a hidden conformal symmetry in the low frequency wave equation for a scalar field in a certain spacetime region referred to as the near region. For extremal case, the near region is expected to be the near horizon region in which the correspondence via the asymptotic symmetry is studied. We investigate the hidden conformal symmetry in the near horizon limit and consider the relation between the hidden conformal symmetry and the asymptotic symmetry in the near horizon limit. By using an appropriate definition of the quasi-local charge, we obtain the deviation of the entropy from the extremality.     

Invariants,singularities, and parameters of a Kerr solution source

The regularity of a basis of algebraic independent second-order invariants of the Riemann-Christoffel tensor of Kerr space-time is proved by direct calculation in a Boyer-Lindquist coordinate system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 40–43, December, 1988.     

The influence of substrate geometry on the emission properties of a liquid metal ion source

The effect of needle radius, cone angle and shaft diameter on the threshold voltage and angular intensity — total current relationships for a Ga liquid-metal ion source (LMIS) was investigated. The variation of threshold voltage with needle geometry could be described in terms of the Taylor theory of liquid cone formation by electrostatic fields. The beam energy spread was mainly a function of total source current and was not a sensitive function of emitter geometry. Source angular intensity at a constant total current increased linearly with threshold voltage when the latter was altered due to source geometry.     

Effect of source geometry on the line contour of reabsorbed radiation

A general relation is derived for the line contour of reabsorbed radiation as a function of the geometric parameters of a cylindrical source and of the optical density of the plasma. The relative intensity of the reabsorbed radiation which leaves the source along its longitudinal axis is also found. A numerical calculation is carried out for a line with a Doppler contour, and it is shown that the Ladenburg-Levi function is a particular case of the function H found in the present analysis. Recommendations are given for improving the accuracy of measurements of the line contour and the integral intensity of the spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp.69–71, March, 1972.     

The Linear Kerr Effect

Russian Physics Journal -     

Charged particle orbits in Kerr geometry with electromagnetic fields as viewed from locally non-rotating frames

The charged particle orbits in electromagnetic fields on Kerr background as viewed from a locally non-rotating frame do not exhibit non-gyrating bound orbits, which was an essential feature in the earlier study of Prasanna and Vishveshwara, thus showing the non gyration to be due to the effect of dragging of inertial frames produced by the rotating black hole.     

The Kerr space-time near the ring singularity

We investigate the geometry of the Kerr space-time near the ring singularity. A systematic study of the mathematical and physical structure of this region reveals that the singularity in the Kerr space-time is naturally understood in terms of a subset of the immersion of the set defined byr=0 (in Boyer-Lindquist coordinates) in the Kerr space-time. It is well known that the Kerr space-time is not a differentiable manifold (due to the curvature singularity) or a topological manifold, but a well defined topological space with a structure that is manifested by the constrast in taking limits along the hypersurface atr=0 and the equatorial plane which approach singularity. We find that the ring singularity is either an edge or a self-intersection of the topological space depending on which extension of the metric throughr=0 is implemented. A major result of this analysis is the extrapolation to the general accelerating case of Carter's proof that the only nonspacelike geodesics which can reach the ring singularity are restricted to the equatorial plane. For finite magnitudes of proper acceleration, it is shown that only lightlike trajectories that asymptotically approach the null generator of the ring singularity can reach it from above or below the equatorial plane.     

The symmetries of Kerr black holes

The Kerr solution describes, in Einstein's theory, the gravitational field of a rotating black hole. The axial symmetry and stationarity of the solution are shown here to arise in a simple way from properties of the curvature tensor.A portion of this work was completed, in part, during the summer of 1972 at the University of Texas at Dallas, Division of Mathematics and Mathematical Physics, and at the Black Hole session of the Ecole d'été de Physique Théorique in Les Houches; supported, in part, by the National Science Foundation, Grants GP-8868, GP-3463 9X, GP-20023, and GU-1598; the Air Force Office of Scientific Research, Grant 903-67; the National Aeronautics and Space Administration, Grant 44-004-001; the Westinghouse Corparation; the Clark Foundation; and the Rhodes Trust at Oxford.     

Energy extraction (a reversible process) from a Kerr source by tachyons

We have demonstrated through a specific example that it is possible to extract rotational energy from a Kerr source (in principle, of arbitrary size but not turned black) through a reversible process by suitably injecting tachyons.     

The Kerr metric in cosmological background

A metric satisfying Einstein’s equations is given which in the vicinity of the source reduces to the well-known Kerr metric and which at large distances reduces to the Robertson-Walker metric of a homogeneous cosmological model. The radius of the event horizon of the Kerr black hole in the cosmological background is found out.