Energy Radiation of Charged Particles in Conformally Flat Spacetimes

Abstract

Original abstract: Consider the worldline of a charged particle in a static spacetime. Contraction of the time-translation Killing field with the retarded electromagnetic energy-momentum tensor gives a conserved electromagnetic energy vector which can be used to define the radiated electromagnetic energy. This note points out that for a conformally flat spacetime, the radiated energy is the same as for a flat spacetime (i.e. Minkowski space). This appears to be inconsistent with an equation of motion for such particles derived by DeWitt and Brehme and later corrected by Hobbs [End of original abstract] New abstract: Same as old abstract with last sentence deleted. The body of the paper is the same as previously. A new Appendix 2 has been added discussing implications to the previous arguments of recent work of Sonego (J. Math. Phys. 40 (1999), 3381-3394) and of Quinn and Wald (Phys. Rev. D 60 (1999), gr-qc/9610053).