Properties of the Deser-Laurent theory of gravitation

Abstract

The flat-space theory of gravitation proposed by Deser and Laurent is studied further. The «Schwarzschild singularity» is closely examined, and found to lead to a real singularity in the behavior of test particles. Two general schemes for the coupling of gravitation to matter are considered. Minimal coupling leads to passive behavior identical with general relativity; fully linearized coupling leads to the result that light no longer follows null geodesics of the effective metric (except to first order), and to apparent inconsistencies in the dogmatic application of kinetic theory. The static interior solution in both coupling schemes is investigated, although not solved exactly. In particular, the nonlocal nature of this theory gives rise to 1/r3 terms in theexterior field. These, however, alter the predictions of the theory only in second-order terms, and never to first order. It is inferred that, as in general relativity, there is a limiting value ofM/R, above which static solutions do not exist. A numerical study of a pressure-free collapsing dust shell shows that matter can, in this theory, travel faster thanc, the velocity of propagation of gravitational waves. Moreover, the shell collapses to within its Schwarzschild radius, though whether it remains there long enough for the formation of a singularity is not ascertained. The Deser-Laurent theory remains a viable if less elegant alternative to general relativity.