On quadratic lagrangians in General Relativity

Theories of gravitation similar to General Relativity but with an additionalR² term in the Lagrangian are explored. The Schwarzschild metric is not the exterior solution that can be continued to the interior of the body to give a positive definite mass distribution. The experimental consequences ofR² terms are investigated. Furthermore, it is shown that a theory with anR² term only possesses an interesting singular dependence on the coupling constant.