Yang's Gravitational Field Equations

Abstract

Yang's gravitational field equations in vacuo can be regarded as "derivative" equations of both Einstein's equations and Nordstr\"om's equations, and embrace all their solutions. Yang's equations admit monopole gravitational radiations; therefore no analog of the Birkhoff theorem can be valid. The most general static spherical-symmetric solution contains four arbitrary parameters. In particular, $d{s}^{2}=\ensuremath{-}d{t}^{2}+{(1+\frac{{c}_{1}}{r}+{c}_{2}{r}^{2})}^{\ensuremath{-}1}d{r}^{2}+{r}^{2}(d{\ensuremath{\theta}}^{2}+{sin}^{2}\ensuremath{\theta}\ifmmode\times\else\texttimes\fi{}d{\ensuremath{\phi}}^{2})$ is a two-parameter exact solution. This metric possesses no gravitational red shifts.