Multipole Moments in General Relativity and Dynamical Perturbations of BlackHole Magnetospheres.
Abstract
This thesis consists of two parts. In part I, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin. The expansion coefficients, called "external multipole moments," are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. The expansion is used to derive higherorder corrections to previously known laws of motion and precession for black holes and other bodies. In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a blackhole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation. More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3 + 1 language in a general spacetime, and reduce the GRMHD equations to a set of algebraic equations for stationary spacetimes and MHD flows with one arbitrary spatial symmetry. Then in a model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the Fourieranalyzed GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These equations are subsequently solved numerically. It is found that when an oscillatory external force is applied to the region of the magnetosphere where plasma (e^+e^ ) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The magnetosphere of a rotating black hole, when perturbed by nonaxisymmetric magnetic fields, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies omega~eq(m/2)Omega_ {rm H} where m is an integer and Omega_{rm H} is the hole's angular velocity.
 Publication:

Ph.D. Thesis
 Pub Date:
 1990
 Bibcode:
 1990PhDT.........1Z
 Keywords:

 Physics: Astronomy and Astrophysics;
 Black Holes (Astronomy);
 Magnetohydrodynamic Flow;
 Magnetospheres;
 Multipoles;
 Perturbation;
 Relativity;
 Riemann Manifold;
 Universe;
 Angular Velocity;
 Fourier Analysis;
 Gravitational Fields;
 Magnetic Fields;
 Magnetohydrodynamic Waves;
 Oscillations;
 Plasmas (Physics);
 SpaceTime Functions;
 Symmetry;
 Vacuum;
 Astrophysics