Ernst formulation of axisymmetric fields in $f(R)$ gravity: applications to neutron stars and gravitational waves

Abstract

The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, non-linear differential equation for a complex-valued scalar function. As a worked example, we apply the generalised Ernst equations to derive a $f(R)$ generalisation 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 $f(R)$ gravity in the context of soliton-like solutions that display shock-wave behaviour across the causal boundary.

arXiv comment12 pages, zero figures. Accepted for publication in PRD

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Cited by in corpus (4)

• Astroseismology of neutron stars from gravitational waves in the limit of perfect measurement
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• A metric on the space of neutron star models in general relativity and modified gravity
• Stable photon orbits in stationary axisymmetric spacetimes with an electromagnetic field and a cosmological constant