Quadratic Langrangians and static gravitational fields

Abstract

AbstractIt is shown that the solutions of the field equations generated by the most general effective quadratic Lagrangian aR2 + bRklRkl which are static, singularity-free, of class C4 and asymptotically flat (of rank A3) are (i) conformally flat when 3a + b = 0, (ii) flat when 3a + b ≠ 0 (b ≠ 0), and (iii) have zero scalar curvature when b = 0.