The Variation of Photon Speed with Photon Frequency in Quantum Gravity
  In the present work, an expression for Planck Mass or Planck Energy is derived by equating the Compton wavelength with the gravitational radius of the Kerr rotating body. Using the modified photon energy-momentum dispersion relation, the variation of the photon propagation speed with photon frequency is derived. It is found that, the photon propagation speed, depends on the frequency of the photon, the rotation parameter of the Kerr rotating body and also on the polarization state of the photon. Quantum gravity effect could be seen from the derived results for the photon propagation speed. 
Anuj Kumar Dubey, A. K. Sen and Sonarekha Nath
gr-qc