Probing general relativistic spin-orbit coupling with gravitational waves from hierarchical triple systems

Wave packets propagating in inhomogeneous media experience a coupling between internal and external degrees of freedom and, as a consequence, follow spin-dependent trajectories. These are known as spin Hall effects, which are well known in optics and condensed matter physics. Similarly, the gravitational spin Hall effect is expected to affect the propagation of gravitational waves on curved spacetimes. In this general-relativistic setup, the curvature of spacetime acts as impurities in a semiconductor or inhomogeneities in an optical medium, leading to a frequency- and polarization-dependent propagation of wave packets. In this letter, we study this effect for strong-field lensed gravitational waves generated in hierarchical triple black hole systems in which a stellar-mass binary merges near a more massive black hole. We calculate how the gravitational spin Hall effect modifies the gravitational waveforms and show its potential for experimental observation. If detected, these effects will bear profound implications for astrophysics and tests of general relativity.