Spherically symmetric solutions to fourth-order theories of gravity

Abstract

Solutions to the field equations 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 will be described, as will the lack of validity of Birkhoff's theorem. Exact solutions are presented which illustrate these points and the stability and equations of motion of particles in these spacetimes are investigated.