http://arxiv.org/abs/2105.08556
Since particles obey wave equations, in general one is not free to postulate that particles move on the geodesics associated with test particles. Rather, for this to be the case one has to be able to derive such behavior starting from the equations of motion that the particles obey, and to do this for either massless or massive particles one can employ the eikonal approximation. While for massive particles one does obtain standard geodesic behavior this way, for a conformally coupled massless scalar field the eikonal approximation only leads to geodesic behavior if the Ricci scalar is zero. Similarly, for the propagation of the light waves associated with the conformal invariant Maxwell equations geodesic behavior only holds if the Ricci tensor is zero. While for practical purposes such terms might only be of relevance in regions of high curvature, the point of this paper is only to establish their presence in principle. Thus in principle the standard null-geodesic-based gravitational bending formula and the behavior of light rays in cosmology are in need of modification in regions with high enough curvature. We show how to appropriately modify the geodesic equations in such situations. We show that relativistic eikonalization has an intrinsic light-front structure, and show that eikonalization in a theory with local conformal symmetry leads to trajectories that are only globally conformally symmetric. The modifications to geodesics that we find lead to the propagation of massless particles off the light cone. This is a curved space reflection of the fact that when light travels through a refractive medium in flat spacetime its velocity is modified from its free flat spacetime value. In the presence of gravity spacetime itself acts as a medium, and this medium can then take light waves off the light cone.
P. Mannheim
Wed, 19 May 21
30/64
Comments: 26 pages
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