P. A. Hogan

The equations of motion of macroscopic bodies in general relativity

A new approach to the problem of motion in General Relativity, based upon the systematic approximation procedure of Synge, is presented. The equations of transnational motion for a system of spherical bodies moving under their mutual gravitational attractions are derived. Approximations are based upon the weakness of the field and on the distance between any two of the bodies being considered large by comparision with their radii. The most general stress distribution consistent with maintaining the symmetry of the bodies throughout the motion is chosen. The use of controlled errors enables us to derive equations of motion applicable to a wider class of physical systems than the original equations of Einstein, Infeld and Hoffmann and Fock-Papapetrou.

Equations of motion in general relativity

1. Introduction 2. Foundations of the Post Newtonian Approximation 3. The Third Post Newtonian Approximation 4. Two-Body Problem in General Relativity 5. Small Black Holes: Geometrical Preliminaries 6. Small Charged Black Holes: Equations of Motion 7. Gravitational Physics of Few Body Systems

Propagation of information by electromagnetic and gravitational waves in cosmology

The propagation of arbitrary information by electromagnetic and gravitational waves in spatially homogeneous and isotropic cosmological models is examined. The test Maxwellian fields and the gravitational perturbations we study depend upon arbitrary functions in the spirit of Trautmans pioneering analysis. We use the covariant and gauge-invariant approach developed by Ellis and Bruni to study cosmological perturbations under this assumption.

A spherical gravitational wave in the de Sitter universe

Abstract An exact solution of Einsteins field equations with a cosmological constant is given describing a spherical-fronted impulsive gravitational wave propagating through the de Sitter universe.

Kaluza–Klein theory derived from a Riemannian submersion

Taking a Riemannian submersion as our starting point, we obtain some formulas derived from O’Neill’s fundamental equations of a submersion and compare them with the basic equations of Bergmann’s approach to Kaluza–Klein theory in five dimensions. Having imposed Hermann’s sufficient conditons for the submersion to be a principal fiber bundle, we study the conclusions that can be drawn from the derived formulas.

Singular Null Hypersurfaces in General Relativity: Light-Like Signals from Violent Astrophysical Events

General Description of an Impulsive Light-Like Signal Illustrations and Implications of the Bianchi Identities Light-Like Boosts Spherically Symmetric Null Shells Collisions of Plane Impulsive Light-Like Signals Impulsive Light-Like Signals in Alternative Theories of Gravity.

Lightlike signals in general relativity and cosmology

The modelling of light-like signals in general relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penroses hierarchical classification of the geometry induced on the null hypersurface history of the signal by its embedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Results are accompanied by illustrative examples using cosmological models, vacuum space-times, the de Sitter universe and Minkowskian space-time.

Advanced general relativity : gravity waves spinning particles and black holes

Preface 1. Minkowskian space-time 2. Plane gravitational waves 3. Equations of motion 4. Inhomogeneous aspects of cosmology 5. Black holes 6. Higher dimensional black holes Appendix A: Notation Appendix B: Transport law For k along r=0 Appendix C: Some useful scalar products References Index

Light-Like 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.

Some physical consequences of abrupt changes in the multipole moments of a gravitating body

An example is described in which an asymptotically flat static vacuum Weyl space-time experiences a sudden change across a null hypersurface in the multipole moments of its isolated axially symmetric source. A light-like shell and an impulsive gravitational wave are identified, both having the null hypersurface as history. The stress-energy in the shell is dominated (at large distance from the source) by the jump in the monopole moment (the mass) of the source with the jump in the dipole moment mainly responsible for the stress being anisotropic. The gravitational wave owes its existence prrincipally to the jump in th quadrupole moment of the source confirming what would be expected. This serves as a model of a cataclysmic astrophysical event such as a supernova.