Geometric Buoyancy-like Effects of Static Structures with Internal Stress in Schwarzschild Spacetime

Abstract

In curved spacetime, deformable bodies can undergo a displacement of their center of mass through cyclic internal motions without the use of propellant, as shown by Wisdom. In this paper, we explicitly construct static structures with internal stress in Schwarzschild spacetime that generate a buoyancy-like force (in the sense of a pressure-imbalance-induced force, but with a different physical origin from fluid buoyancy) purely from stress distribution, without non-gravitational external forces or cyclic internal motions. The mechanism is illustrated using simple static structures composed of rod-like elements aligned along spatial geodesics with assigned internal stresses, for which both numerical calculations and perturbative analyses are performed. The resulting effect is extremely small for realistically sized structures and does not lead to actual ascent against gravity. Nevertheless, it reveals a new aspect of extended-body dynamics in curved spacetimes, namely how stress-curvature coupling can influence motion of extended bodies even in static configurations.