Conformally flat zero-mass meson solutions of Einstein equations

The field equations for the coupled zero-mass scalar field and gravitational fields are solved in the conformally flat situation. The scalar field gradient is taken to be proportional to the gradient of the metric coefficient. The solution is found to be $d{s}^2=(a_i{x}^i+1)ds_0^{}{}_{}{}^2$, where $d{s}_0$ is defined to be flat space-time.