Black holes and wormholes in $f(R)$ gravity with a kinetic curvature scalar

TL;DR

This paper explores spherically symmetric solutions in a modified gravity model derived from $f(R)$ gravity with a kinetic scalar, analyzing horizons, centers, and asymptotic behavior, and comparing with existing solutions.

Contribution

It introduces new classes of solutions in $f(R)$ gravity with a kinetic scalar, including cases with zero and non-zero potentials, using harmonic coordinates and specific ansatz.

Findings

Identified solutions with zero potential and analyzed their properties.

Found new solutions with non-zero potential using a specific metric relation.

Compared these solutions with previous literature to highlight differences.

Abstract

We study the chiral self-gravitating model (CSGM) of a special type in the spherically symmetric static spacetime in Einstein frame. Such CSGM is derived, by virtue of Weyl conformal transformation, from a gravity model in the Jordan frame corresponding to a modified $f(R)$ gravity with a kinetic scalar curvature. We investigate the model using harmonic coordinates and consider a special case of the scaling transformation from the Jordan frame. We find classes of solutions corresponding to a zero potential and we investigate horizons, centers and the asymptotic behavior of the obtained solutions. Other classes of solutions (for the potential not equal to zero) are found using a special relation (ansatz) between the metric components. Investigations of horizons, centers and asymptotic behavior of obtained solutions for this new case are performed as well. Comparative analysis with the solutions obtained earlier in literature is made.