Possible quantum gravity effects on the gravitational deflection of light

Abstract

We investigate possible quantum gravity (QG) effects on the gravitational deflection of light. Two forms of deformation of the Schwarzschild spacetime are proposed. The first ansatz is a given Finslerian line element, it could be regarded as a weak QG effect on the Schwarzschild spacetime. Starting from this ansatz, we deduce the deflection angle of the light ray which passes a weak gravitational source. The second ansatz could be regarded as a strong QG effect on the Schwarzschild spacetime. The deflection angle of the light ray which passes a weak gravitational source is deduced in this Riemannian spacetime. This QG effect may distinguish the mixed light rays in the absence of gravitational source by a "spectroscope" (the gravitational source). The solutions of gravitational field equation in this Riemannian spacetime indicate that the QG effect could be regarded as the vacuum energy and the energy density of vacuum is related to the spacetime deformation parameter.

References in corpus (6)

• Dynamics of dark energy
• Planck-scale modified dispersion relations and Finsler geometry
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
• Lorentz Invariance Violation and Symmetry in Randers--Finsler Spaces
• Catching a bullet: direct evidence for the existence of dark matter