Initial data for Einstein's equations with superposed gravitational waves
A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with linear gravitational waves, and allows detailed control over characteristics of the superposed gravitational wave like shape, location and propagation direction. It is furthermore fully covariant with respect to spatial coordinate changes and allows for very large amplitude of the gravitational wave.
©2005 The American Physical Society (Received 4 October 2004; revised 7 December 2004; published 20 January 2005) It is a pleasure to acknowledge helpful discussions with Lee Lindblom, Saul Teukolsky and Jimmy York. This work was supported in part by NSF Grants No. PHY-9900672 at Cornell, No. PHY-0099568 and No. PHY-0244906 at Caltech and No. PHY-0354821 at Penn State. D. S. acknowledges the support of the Center for Gravitational Wave Physics funded by NSF No. PHY-0114375.