Gravitational Aharonov-Bohm phase in Kalb-Ramond spacetimes

We study two complementary signatures of a gravitational Aharonov-Bohm (AB) effect in a Kalb-Ramond (KR)-deformed, static, spherical spacetime. In free fall, a compact quantum system on a slightly eccentric low-Earth orbit acquires a purely scalar AB phase that frequency-modulates stationary levels into evenly spaced sidebands. The spacing is set by the orbital frequency, while the envelope scales linearly with the KR deformation. Sensitivity estimates show that state-of-the-art atomic clocks and Mossbauer spectroscopy can detect these signals. For null waves grazing the photon sphere, each extra winding adds one orbital period of phase, producing a spectral comb in interferometric visibility with spacing set by the photon-sphere frequency and an exponentially damped envelope (Lyapunov rate). In KR geometry the shadow shrinks while the comb spacing grows, preserving an exact duality. Forecasts for Sgr A* and M87* indicate that joint shadow-comb measurements tightly bound Lorentz-violating departures from Schwarzschild gravity.