The Energy Dependence of Micro Black Hole Horizon in Quantum Gravity Theory

The energy dependence of the deflection angle is a common prediction in some quantum gravity theories when the impact parameters are much larger than the photon wavelength. For low energy photons, the deflection angle recovers to the prediction of GR. But it reduces to zero for infinite energy photons. In this paper, we develop an effective approach to calculate the trajectory of photons and other deflection-related quantities semiclassically by replacing $h_{\mu \nu}$ with $h_{\mu \nu} \times f(E)$ to include the correction of quantum gravity. This approach could provide more information for photons traveling in an external gravitational field. We compute the horizon of micro black hole with this method and find that they are all energy dependent and decrease to zero as the energy increases to infinity.