Linearised R+R2 gravity: a new gauge and new solutions

Abstract

The author studies the linearised fourth-order field equations for gravitational theories with Lagrangians L=-g(R+1/2aR2+bRmu nu Rmu nu )- kappa Lm. He shows that a suitable choice of coordinate conditions involving third derivatives of the potentials leads directly to the general solution of these equations. He states appropriate junction conditions across a timelike (or spacelike) hypersurface of discontinuity. Using these junction conditions, and assuming the metric to be asymptotically flat at spatial infinity, he determines the potentials of an isolated static body in the case 3a+2b<or=0, b>or=0. The new gauge yields the corresponding metric in a spatially isotropic form. These results are applied to a static spherically symmetric body: the potentials are obtained in a simple integral form when the rest-mass density of matter depends upon the distance from the centre. The results previously obtained for a pointlike distribution of matter and for a homogeneous sphere become trivial consequences of the general method.