Spherically Symmetric Solutions to Fourth-Order Theories of Gravity

TL;DR

This paper explores spherically symmetric solutions in f(R) gravity theories, highlighting differences from Schwarzschild solutions, and investigates their stability, geodesics, and the breakdown of Birkhoff's theorem.

Contribution

It provides new exact solutions in f(R) gravity and analyzes their properties, including stability and geodesic behavior, contrasting with standard General Relativity.

Findings

Exact spherically symmetric solutions differ from Schwarzschild

Birkhoff's theorem does not hold in these theories

Solutions exhibit unique asymptotic behaviors

Abstract

Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild solution. The asymptotic form of solutions is described, as is the lack of validity of Birkhoff's theorem. Exact solutions are presented which illustrate these points and their stability and geodesics are investigated.