Formula_21189

\[\left\{\begin{array}{l}(\operatorname{re} \mathscr{E}+\Phi \bar{\Phi}) \eta^{\mu v}\left(\partial_{\mu}+\frac{\alpha_{\mu}}{\alpha}\right) \partial_{v} \mathscr{E}-\eta^{\mu v}\left(\partial_{\mu}^{\mathscr{E}}+2 \bar{\Phi} \partial_{\mu} \Phi\right) \partial_{v} \mathscr{E}=0, \\ (\operatorname{Re} \mathscr{E}+\Phi \bar{\Phi}) \eta^{\mu v}\left(\partial_{\mu}+\frac{\alpha_{\mu}}{\alpha}\right) \partial_{v} \Phi-\eta^{\mu v}\left(\partial_{\mu} \mathscr{E}+2 \bar{\Phi} \partial_{\mu} \Phi\right) \partial_{v} \Phi=0\end{array}\right.\]