Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes

TL;DR

This work introduces the equatorial planetoid string Ansatz in stationary axisymmetric 3+1 spacetimes and derives exact quadrature expressions for the classical and semiclassical (WKB) dynamics. By analyzing explicit solutions in Minkowski, static Robertson–Walker, de Sitter, anti-de Sitter, and Schwarzschild spacetimes, it reveals non-linear Regge trajectories and horizon-induced constraints such as finite bound-state spectra and minimum angular momentum. The results show how curvature and horizons qualitatively modify the string spectrum, offering insight into string behavior in curved backgrounds and potential implications for quantum gravity regimes. Overall, the planetoid approach provides a tractable framework to explore the interplay between gravity, string tension, and rotation in diverse spacetimes.

Abstract

The string propagation equations in axisymmetric spacetimes are exactly solved by quadratures for a planetoid Ansatz. This is a straight non-oscillating 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/(mass$^2$) (Regge) relation for the planetoids, which turns out to be non-linear.