Spacetime geometry fluctuations and 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

Spacetime and Euclidean Geometry

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem. Introduction Spacetime dia...

Geodesic laminations and noncommutative geometry

Measured geodesic laminations is a remarkable abstraction (due to W. P. Thurston) of many otherwise unrelated phenomena occurring in differential geometry, complex analysis and geometric topology. In this article we focus on connections of geodesic laminations with the inductive limits of finite-dimensional semi-simple C∗-algebras (AF C∗-algebras). Our main result is a bijection between combina...

Deviation of geodesics in FLRW spacetime geometries

The geodesic deviation equation (‘GDE’) provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the Friedmann–Lemâıtre–Robertson–Walker (‘FLRW’) models, where we assume the sources to be given by a non-interacting mixture of incoherent matter and radiation, and we also take a non-zero co...