Spherically symmetric vacuum solutions of modified gravity theory in higher dimensions

TL;DR

This paper explores spherically symmetric vacuum solutions in higher-dimensional $f(R)$ gravity, deriving exact and approximate solutions depending on the form of the function $F(R)$, advancing understanding of modified gravity in extra dimensions.

Contribution

It provides explicit solutions for $f(R)$ gravity in higher dimensions, including exact solutions for specific functions and approximate solutions for more general cases.

Findings

Exact solutions for specific $F(R)$ functions.

Approximate metric solutions near $F(R) o 1$.

Enhanced understanding of higher-dimensional modified gravity.

Abstract

In this paper we investigate spherically symmetric vacuum solutions of $f(R)$ gravity in a higher dimensional spacetime. With this objective we construct a system of non-linear differential equations, whose solutions depend on the explicit form assumed for the function $F(R)=\frac{df(R)}{dR}$. We explicit show that for specific classes of this function exact solutions from the field equations are obtained; also we find approximated results for the metric tensor for more general cases admitting $F(R)$ close to the unity.