The Upper Kilohertz Quasi-periodic Oscillation: A Gravitationally Lensed Vertical Oscillation

We show that a luminous torus in the Schwarzschild metric oscillating along its own axis gives rise to a periodically varying flux of radiation, even though the source of radiation is steady and perfectly axisymmetric. This implies that the simplest oscillation mode in an accretion flow, axisymmetric up-and-down motion at the meridional epicyclic frequency, may be directly observable when it occurs in the inner parts of accretion flow around neutron stars and black holes. The high-frequency modulations of the X-ray flux observed in low-mass X-ray binaries at two frequencies (twin kHz QPOs) could then be a signature of strong gravity both because radial and meridional oscillations have different frequencies in non-Newtonian gravity, and because strong gravitational deflection of light rays causes the flux of radiation to be modulated at the higher frequency