Relativistic global navigation satellite system

BMS-invariant wave equations

• Evangelos Melas

• University of Athens

The standard approach to gravitational waves produced by a distant source assumes that the Minkowski metric is perturbed by the incoming wave as g_μν = η_μν + ε h_μν , with ε²<<ε. Replacing this in the vacuum Einstein’s equations and using the de Donder gauge, we obtain the well-known linear wave equation in Minkowski’s space–time. On the other hand, since the supertranslations depend on the source’s rotation, the asymptotically flat BMS-invariant metric also carries informations on that rotation angle. The general expression of the BMS-invariant metric βμν has been shown to be not invariant under the Poincar´e group, except in the particular case when the source collapses into a spherically symmetric system It follows that the correct wave equation will also be invariant under the BMS group, written with the BMS-invariant metric. Presumably this is not the wave equation used in LIGO considerations. Therefore it is likely that some corrections should be made. With this motivation BMS-invariant wave equations are derived.