A local reconstruction framework maps Φ(R,φ,X) theories to f(R,ℛ) hybrid gravity in the Einstein frame, with the inverse mapping non-unique and parametrized by kinetic coupling.
A study of cylindrically symmetric solutions inf(R, ϕ, X)theory of gravity
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Reconstruction Between Generalized Hybrid Metric--Palatini Gravity and $\Phi(R,\phi,X)$ Theories
A local reconstruction framework maps Φ(R,φ,X) theories to f(R,ℛ) hybrid gravity in the Einstein frame, with the inverse mapping non-unique and parametrized by kinetic coupling.