General relativity. Papers in honour of J._L._Synge.

A technique for extracting from the appropriate field equations the relativistic motion of Schwarzschild, Reissner-Nordstrom and Kerr particles moving in external fields is motivated and illustrated. The key assumptions are that (a) the particles are isolated and (b) near the particles the wave fronts of the radiation generated by their motion are smoothly deformed spheres. No divergent integrals arise in this approach. The particles are not test particles. The formalism is used, however, to derive the Mathisson–Papapetrou equations of motion of spinning test particles, neglecting spin–spin terms.

Equations of Motion of Schwarzschild, Reissner-Nordström and Kerr Particles

This paper deals with exact solutions of the Einstein–Maxwell equations. The solutions belong to a metric form which is a special case of the Robinson–Trautman form. The chosen metric form admits positive, zero, and negative Gaussian curvature (labeled e=1, 0, −1, respectively) of its two‐dimensional angularlike part. Some general properties of the solutions are given for all the values of e. All the explicit solutions for e=±1 are presented. They are of the Petrov type II. The physical meaning of e is discussed.

On a certain class of solutions of the Einstein–Maxwell equations

The application of the ideas of the symmetry classification of space‐time, the algebraic classification of the energy‐momentum tensor, and the dominant energy conditions for macroscopic matter to the problem of searching for solutions to the field equations of general relativity is discussed. These ideas are then specifically applied to certain space‐times of G4 symmetry to demonstrate the ability of this approach to obtain both new and general solutions. For macroscopic matter, G4I1 symmetry is shown to have only one general solution; symmetries G4V, G4VII1, and G4VII2 are shown to allow no solutions whatever; and the method is used to discover a new solution for G4VIII1 symmetry. A similar solution would be expected for G4VIII2 symmetry.

On the application of energy conditions and algebraic classification in general relativity

Considers the linearised gravitational and electromagnetic fields of an axially symmetric charged source which is rotating about its symmetry axis and moving with arbitrary acceleration along its symmetry axis when viewed in the flat background space-time. It is established that if the linearised field of the body and the linearised twist of the degenerate principal null direction of the Weyl tensor are 'wire' singularity-free, then the body must either move with zero acceleration or perform runaway motion from an unaccelerated state in the infinite past, and its mass and charge are constant at lowest order. Also, its rotation is either uniform or singular in the infinite past.

https://iopscience.iop.org/article/10.1088/0305-4470/13/5/033/pdf

G.M. O'Brien

Papers

On the motion of rotating bodies in linearized gravity

Some Robinson-Trautman solutions of the Einstein-Maxwell equations

An Einstein-Maxwell field with null fluid present