Abstract
The Ernst formulation of the Einstein equations is generalized to accommodate theories of gravity. It is shown that, as in general relativity, the axisymmetric field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, nonlinear differential equation for a complex-valued scalar function. As a worked example, we apply the generalized Ernst equations to derive a generalization of the Zipoy-Voorhees metric, which may be used to describe the gravitational field outside of an ellipsoidal neutron star. We also apply the theory to investigate the phase speed of large-amplitude gravitational waves in gravity in the context of solitonlike solutions that display shock-wave behavior across the causal boundary.
- Received 26 May 2016
DOI:https://doi.org/10.1103/PhysRevD.94.044045
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