Eguchi-Hanson like space-times in F(R) gravity

TL;DR

This paper explores Eguchi-Hanson type instanton solutions within an extended F(R) gravity model, deriving exact solutions and analyzing their stability and asymptotic behavior in four and five dimensions.

Contribution

It introduces new analytic Eguchi-Hanson solutions in F(R) gravity with exponential and power corrections, extending previous models and analyzing their stability.

Findings

Found four-dimensional Eguchi-Hanson instanton solutions in F(R) gravity.

Derived exact five-dimensional solutions with Eguchi-Hanson hypersurfaces.

Confirmed Dolgov-Kawasaki stability of the solutions.

Abstract

We consider a model of $F(R)$ gravity in which exponential and power corrections to Einstein-$\Lambda$ gravity are included. We show that this model has 4-dimensional Eguchi-Hanson type instanton solutions in Euclidean space. We then seek solutions to the five dimensional equations for which space-time contains a hypersurface corresponding to the Eguchi-Hanson space. We obtain analytic solutions of the $F(R)$ gravitational field equations, and by assuming certain relationships between the model parameters and integration constants, find several classes of exact solutions. Finally, we investigate the asymptotic behavior of the solutions and compute the second derivative of the $F(R)$ function with respect to the Ricci scalar to confirm Dolgov-Kawasaki stability.