DYNAMICS OF GRAVITATIONAL-WAVES IN 3D - FORMULATIONS, METHODS, AND TESTS

The dynamics of gravitational waves is investigated in full (3 + 1)-di mensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising fr om nonlinearities and gauge degrees of freedom. Using gravitational wa ves with amplitudes low enough that one has a good understanding of th e physics involved, but large enough to enable nonlinear effects to em erge, we study the coupling between numerical errors, coordinate effec ts, and the nonlinearities of the theory. We discuss the various strat egies used in identifying specific features of the evolution. We show the importance of the flexibility of being able to use different numer ical schemes, different slicing conditions, different formulations of the Einstein equations [standard Arnowitt. Deser, and Misner vs first order hyperbolic], and different sets of equations (linearized vs full Einstein equations). A nonlinear scalar field equation is presented w hich captures some properties of the full Einstein equations, and has been useful in our understanding of the coupling between finite differ encing errors and nonlinearities. We present a set of monitoring devic es which have been crucial in our studying of the waves. including Rie mann invariants, pseudo-energy-momentum tensor, Hamiltonian constraint violation, and Fourier spectrum analysis.