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Wave packets propagating in inhomogeneous media experience a coupling betweeninternal and external degrees of freedom and, as a consequence, followspin-dependent trajectories. These are known as spin Hall effects, which arewell known in optics and condensed matter physics. Similarly, the gravitationalspin Hall effect is expected to affect the propagation of gravitational waveson curved spacetimes. In this general-relativistic setup, the curvature ofspacetime acts as impurities in a semiconductor or inhomogeneities in anoptical medium, leading to a frequency- and polarization-dependent propagationof wave packets. In this letter, we study this effect for strong-field lensedgravitational waves generated in hierarchical triple black hole systems inwhich a stellar-mass binary merges near a more massive black hole. We calculatehow the gravitational spin Hall effect modifies the gravitational waveforms andshow its potential for experimental observation. If detected, these effectswill bear profound implications for astrophysics and tests of generalrelativity.

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