Gravitational waves: The nonlinearized theory

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Abstract
A simple reformulation of general relativity is developed by dividing the geometry of space-time into a background part and a gravitational-wave part and forgoing any weak-field approximations. A study of the resulting formalism uncovers three main features: (1) Einstein's field equation can be derived from a Lagrangian which is a scalar density, but which depends only upon certain Lagrange coordinates and their first derivatives, (2) two new divergence relations arise from the coordinate invariance of the wave-background action, and (3) a symmetric energy-momentum tensor can be naturally associated with the waves. Various aspects of the nonlinearized theory are compared with their counterparts in earlier studies of relativity and gravitational waves.