Planetoid string solutions in 3+1 axisymmetric spacetimes

The string propagation equations in axisymmetric spacetimes are exactly solved by quadratures for a planetoid ansatz. This is a straight nonoscillating string, radially disposed which rotates uniformly around the symmetry axis of the spacetime. In Schwarzschild black holes, the string stays outside the horizon pointing towards the origin. In de Sitter spacetime the planetoid rotates around its center. We quantize semiclassically these solutions and analyze the spin/(${\mathrm{mass}}^2$) (Regge) relation for the planetoids, which turns out to be nonlinear.