Ernst formulation of axisymmetric fields inf(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.

A metric on the space of neutron star models in general relativity and modified gravity

“…If some compact hypersurface M ⊂ M can be constructed in an invariant manner which captures the black hole physics, or if suitably decaying conformal factors can be introduced so that (1) converges [31,32], the formalism developed here would largely carry over. This could be used to quantify the 'closeness' of black hole models in different modified theories of gravity [40][41][42].…”

“…build h ij from e 2Ω κ µν with conformal factor Ω decaying sufficiently rapidly so that (1) converges) [30], the formalism developed here would largely carry over. This could be used to quantify the 'closeness' of black hole models in different modified theories of gravity [42][43][44].…”

Astroseismology of neutron stars from gravitational waves in the limit of perfect measurement

“…It would also be worthwhile considering whether isospectral stars in modified theories of gravity can exist, since the properties of GWs can vary Suvorov & Melatos 2017). The solution generating techniques discussed by Suvorov & Melatos (2016) may be useful in this direction.…”

Causal properties of nonlinear gravitational waves in modified gravity

“…where ψ and γ are functions of t and ρ [1,29]. In GR, vacuum GW solutions, represented by (10) or otherwise, must necessarily have unit propagation speed (see Theorem 8.8 of [32]).…”

“…Given the well-studied equivalence between f (R) and scalar-tensor theories of gravity, it is reasonable to expect a similar phenomenon to occur in f (R) gravity depending on the particulars of the function f [14]. Hence, one must be careful when drawing conclusions about nonlinear GWs from analysis of the corresponding linearised field equations [29,30]. This phenomenon is related to the Vainshtein mechanism [31].…”