Larmor formula in curved spaces

Abstract

The energy-momentum tensor of the field produced by an electron with arbitrary movement in a curved space contains a tensor Tμνr with the following properties: (i) vanishing covariant divergence, (ii) null flux across the cones that come out from the world line of the electron, and (iii) positive-definite diagonal elements of Tμνr. These properties make it possible to express the differential conservation law in an integral form over a two-dimensional surface contained in the cone with apex in a fixed point of the world line of the electron. This integral gives a measure of the energy irreversibly emitted by the electron associated to the tensor Tμνr. The corresponding rate of radiation is given by 23 e2|z2, where z2 is the square of the covariant acceleration