Gravitational Orbital Hall Effect of Vortex Photons in Lense-Thirring Metric

Vortex photons, possessing an intrinsic orbital angular momentum (OAM) aligned with the direction of propagation, are described using vortex electromagnetic wave packets. Similar to the gravitational spin Hall effect (SHE), these vortex photons are expected to exhibit intrinsic OAM-dependent trajectories and separations when propagating through a gravitational field, a phenomenon termed the gravitational orbital Hall effect (OHE). In this work, we construct a vortex Laguerre-Gaussian electromagnetic wave packet and analyze its motion by solving covariant Maxwell equations within the Lense-Thirring metric. Our findings reveal that vortex photons with different intrinsic OAM not only separate perpendicular to the null geodesic plane but also within it. This behavior contrasts with the gravitational SHE, where photons of opposite spins separate primarily perpendicular to the null geodesic plane. Moreover, the relationship between the separation and intrinsic OAM differs significantly from that between the separation and spin. These results suggest a unique interaction between intrinsic OAM and gravity, distinct from the spin-gravity coupling, indicating that the gravitational OHE might not be precisely predicted by merely substituting spin with intrinsic OAM in the gravitational SHE.