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

We study the linearised fourth-order field equations for gravitational theories with Lagrangians of the form R + R2. We show that a suitable choice of coordinate conditions involving third derivatives of the potentials leads directly to the general solution of these equations. We state 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, we determine the potentials of an isolated static body in the case 3a + 2b ≤ O, b ≥ O. The new gauge yields the corresponding metric in a spatially isotropic form. These results are applied to a static spherically symmetric body. (author)