Gravitational field of spherical domain walls (Q1596262)

The authors consider a spherically symmetric domain wall with non vanishing stress component in the direction perpendicular to the plane of the wall. The domain wall is characterized by the energy momentum tensor \(T_{\mu\nu }=\rho (g_{\mu\nu }+\zeta_{\mu }\zeta_{\gamma })+p_1\zeta_{\mu }\zeta_{\gamma }\), where \(p_1\) is the pressure in the direction normal to the plane of the wall and \(\zeta_{\mu }\) is a unit space-like vector in the same direction. Thus the momentum tensor takes the form \(T_t^r=0\), \(T_t^t=T_{\theta }^{\theta }=T_{\Phi }^{\Phi }=\rho \), \(T_r^r=-p_1\) (\(\rho \) is the energy density of the wall). The exact solutions are obtained using functional separability of the metric coefficients. The motion of the test particles in different situations is studied as well.