General-Relativistic Corrections on the Optical Measurement of the Earth-Fixed Rotating Observer in the Schwarzschild Background

We investigate the behavior of light rays in a rotating observer’s frame in the Schwarzschild background. We derive the null geodesic equations and effective potential for photons in this space-time and then use them to investigate the radial and circular motion of light and its coordinate velocity. Then, we investigate some phenomena related to the motion of light in this space-time, including the Sagnac effect, the radar echo experiment, the gravitational redshift, and the gravitational analog of the space-time index of refraction. In all cases, for the Earth-fixed rotating observer, we calculate the corrections due to the Earth’s rotation (which appear through the rotational coordinate transformation), and the general-relativistic corrections that are obtained by assuming the Schwarzschild background.