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

TL;DR

This paper demonstrates that static structures with internal stress in Schwarzschild spacetime can produce a buoyancy-like force purely from stress distribution, revealing new stress-curvature effects in extended-body dynamics.

Contribution

It explicitly constructs static, stressed structures in Schwarzschild spacetime that generate buoyancy-like forces without external forces or cyclic motions.

Findings

Stress-curvature coupling influences extended-body motion in static configurations.

Numerical and perturbative analyses confirm the buoyancy-like effect.

The effect is extremely small for realistic structures, not causing ascent against gravity.

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.