We investigate the gravitational Lagrangian $L_G=\left(\frac{c^4}{16\pi G}\right)R-\left(\frac{\hslash c}{16\pi {\alpha }_G}\right) {R^{\alpha }}_{\beta \gamma \delta } {R_{\alpha }}^{\beta \gamma \delta }$, where the curvatures are computed from a metric-compatible connection with torsion. We prove that the Schwarzschild metric and its torsion-free connection constitute the unique O(3) spherically symmetric (including reflections) solution to the vacuum field equations of $L_G$.

• Received 5 June 1978

DOI:https://doi.org/10.1103/PhysRevD.19.2264