  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.
