Static plane-symmetric solutions for self-gravitating nonlinear scalar fields

Summary: "We consider in the plane-symmetric metric the set of gravitational and scalar field equations with the nonlinear term dV(phi)/dphi in the scalar field equation, where V(phi) is an arbitrary function, and suggest an approach to finding exact solutions. In this approach the set of equations is reduced to an equation relating the metric tensor component g_{11}(x)=-exp[2alpha(x)] to V(phi). The resulting equation can be used for determining V(phi) for a given function alpha=Gamma(phi), or for determining alpha=Gamma(phi) for a given function V(phi). In the first case we obtain the general solution of the original equation, and in the second case the original equation can be reduced to an abelian equation of the first kind. In this approach we obtain exact self-consistent solutions to the equations which, in flat space-time, turn into the Klein-Gordon and sine-Gordon equations [T. Schneider and E. Stoll, Phys. Rev. Lett. {bf 41} (1978), no. 21, 1429--1432]."