Spherically Symmetric Solutions of a Chiral Self-Gravitating Model in $$\boldsymbol{f(R,\square R)}$$ Gravity

Abstract

We study modified f (R, (∇R) 2 , R) gravity and show in detail how it can be reduced to Einstein gravity with a few scalar fields and then represented in the form of chiral self-gravitating model of the special type. In further investigation of the model we focus on cosmology and looking for solutions of the dynamic equations of chiral fields and the Einstein-Friedman equations in the Friedman-Robertson-Walker spacetime. Exact solutions of the considered model for zero and constant potential are found. Between them power law solution corresponded to equation of state for radiation dominated Universe, de Sitter solution, trigonometric and hyperbolic expansion solution. Various type of chiral fields evolution support listed above solutions.

Spherically Symmetric Space-Times in Generalized Hybrid Metric-Palatini Gravity

“…It is clear that the present results are applicable to many more particular STT because the boundaryvalue problems 1 and 2 for spherical perturbations emerge under quite general conditions. In particular, it is true for various STT representations of various modified theories of gravity other than STT as such, for example, the original [26] and generalized [27] versions of hybrid metric-Palatini gravity, for which static, spherically symmetric solutions are discussed in [28,29], as well as different models of nonlocal and high-order gravity, see, e.g., [30][31][32][33].…”