EQUATIONS OF MOTION IN LINEARIZED GRAVITY .1. UNIFORM ACCELERATION

The authors describe a straightforward approach to studying the motion of the sources of some Robinson-Trautman gravitational fields (1962) in linearised gravity. It involves expanding the Robinson-Trautman line-element about Minkowskian space-time in powers of a small parameter (the 'mass' of the source). They solve the linearised field equation in vacuo by first specifying the source world-line in the background Minkowskian space-time. Functions of integration are determined by the requirement that terms be excluded from the field (Riemann tensor) of the particle which are singular along null-rays emanating into the future from events on the source world-line in the background space-time. As an example they take the world-line to be the history of a uniformly accelerated particle. They show that the solution agrees with the exact solution of Levi-Civita to this problem, in the linear approximation.