The upper kilohertz quasi-periodic oscillation: A gravitationally lensed vertical oscillation

We show that a luminous torus orbiting a Schwarzschild black hole gives rise to a periodically varying flux of radiation when oscillating along its own axis, 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 kilohertz quasi-periodic oscillations) 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.