arXiv subjects
Publications and source records attributed to W. B. Bonnor.
Many solutions of Einstein's field equations contain closed timelike curves (CTC). Some of these solutions refer to ordinary materials in situations which might occur in the laboratory, or in astrophysics. It is argued that, in default of a reasonable interpretation of CTC, general relativity does not give a satisfactory account of all phenomena within its terms of reference.
Using Einstein-Maxwell theory I investigate the gravitational field generated by an electric charge and a magnetic dipole, both held in fixed positions, but spinning with prescribed angular momenta. There is a conical singularity between them representing a strut balancing the gravitational attraction of their masses. However, there is in general another singularity, which I call a torsion singularity. I interpret this as a couple needed to maintain the spins at their prescribed values. It vanishes when the parameters obey a certain formula. A conclusion of the work is that the charge and the magnet must spin relative to one another unless constrained by a couple.
I derive an exact, static, axially symmetric solution of the Einstein-Maxwell equations representing two massless magnetic dipoles, and compare it with the corresponding solution of Einstein's equations for two massless spinning particles (see gr-qc/0201094). I then obtain an exact stationary solution of the Einstein-Maxwell equations representing two massless spinning magnets in balance. The conclusion is that the spin-spin force is analogous to the force between two magnetic dipoles, but of opposite sign, and that the latter agrees with the classical value in the first approximation.
I obtain an exact, axially symmetric, stationary solution of Einstein's equations for two massless spinning particles. The term representing the spin-spin interaction agrees with recently published approximate work. The spin-spin force appears to be proportional to the inverse fourth power of the coordinate distance between the particles.
We match the vacuum, stationary, cylindrically symmetric solution of Einstein's field equations with $Λ$, in a form recently given by Santos, as an exterior to an infinite cylinder of dust cut out of a Gödel universe. There are three cases, depending on the radius of the cylinder. Closed timelike curves are present in the exteriors of some of the solutions. There is a considerable similarity between the spacetimes investigated here and those of van Stockum referring to an infinite cylinder of rotating dust matched to vacuum, with $Λ=0$.
We consider a burst of quadrupole gravitational radiation in the presence of a large static mass $M$ situated at its source. Some of the radiation is back-scattered off the static field of the large mass, forming a wave tail. After the burst, the tail is a pure incoming wave, carrying energy back towards the source. We calculate this energy, and, in a numerical example, compare it with the outgoing wave energy. If $M$ is sufficiently large the incoming energy can equal the outgoing energy, indicating that the primary outgoing wave is completely suppressed.
Einstein's equations admit solutions corresponding to photon rockets. In these a massive particle recoils because of the anisotropic emission of photons. In this paper we ask whether rocket motion can be powered only by the emission of gravitational waves. We use the double series approximation method and show that this is possible. A loss of mass and gain in momentum arise in the second approximation because of the emission of quadrupole and octupole waves.
Einstein's vacuum equations are solved up to the second approximation for imploding quadrupole gravitational waves. The implosion generates a black hole singularity irrespective of the strength of the waves.