Spherical symmetric solutions of $f(R)$ gravity with a kinetic curvature scalar

TL;DR

This paper explores spherically symmetric solutions in a modified $f(R)$ gravity model with a kinetic curvature scalar, focusing on transformations between frames and proposing a method to determine the kinetic function.

Contribution

It introduces a method to determine the kinetic function based on scalar field dependence and finds new classes of solutions for specific $f(R)$ functions.

Findings

New classes of solutions for specific $f(R)$ functions

Method for determining kinetic function from scalar field dependence

Analysis of solutions in Einstein and Jordan frames

Abstract

We consider modified $f(R)$ gravity with a kinetic curvature scalar as a chiral self-gravitating model in a spherically symmetric spacetime. Most attention devoted to finding solutions for special case of scaling transformation when modified gravity transforms to Einstein frame from Jordan one. We proposed the method of determination of kinetic function for given scalar field dependence on space coordinate. New classes of solutions are found for special choice of $f(R)$ function.