The quantization of geodesic deviation

The Quantization of Geodesic Deviation

There exists a two parameter action, the variation of which produces both the geodesic equation and the geodesic deviation equation. In this paper it is shown that this action can be quantized by the canonical method, resulting in equations which generalize the Klein-Gordon equation. The resulting equations might have applications, and also show that entirely unexpected systems can be quantized...

Geodesic Deviation and Weak-Field Solutions

Geodesic Deviation of Photons in Einstein and Higher Derivative Gravity

We derive the wave equation obeyed by electromagnetic fields in curved spacetime. We find that there are Riemann and Ricci curvature coupling terms to the photon polarisation which result in a polarisation dependent deviation of the photon trajectories from null geodesics. Photons are found to have an effective mass in an external gravitational field and their velocity in an inertial frame is i...

A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves

where (u, v) and (x, y) is a pair of null and (transverse) Cartesian coordinates respectively, and f denotes the profile function subject to the field equations. Hence the spacetime is flat everywhere except for the null hypersurface u = 0, where it has a δ-like pulse modelling a gravitational shock wave. Such geometries arise most naturally as ultrarelativistic limits of boosted black hole spa...

Institute for Mathematical Physics a Rigorous Solution Concept for Geodesic and Geodesic Deviation Equations in Impulsive Gravitational Waves a Rigorous Solution Concept for Geodesic and Geodesic Deviation Equations in Impulsive Gravitational Waves

The geodesic as well as the geodesic deviation equation for impulsive gravi-tational waves involve highly singular products of distributions (, 2 , 2). A solution concept for these equations based on embedding the distributional metric into the Colombeau algebra of generalized functions is presented. Using a universal regularization procedure we prove existence and uniqueness results and calcul...