de Sitter geodesics

Abstract

The geodesics on the (1 + 3)-dimensional de Sitter spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lemaître-Robertson-Walker, de Sitter-Painlevé and static local charts with Cartesian space coordinates. Moreover, it is shown that there exist a special static chart in which the geodesics are genuine hyperbolas whose asymptotes are given by the conserved momentum and the associated dual momentum.

Collective classical motion on hyperbolic spacetimes of any dimensions

“…We recover thus our previous result obtained recently for d = 3 [5]. In addition, we obtain the momentum components,…”

“…In our investigations we observed that on dS and AdS spacetimes there are special static charts [8,9] with Cartesian coordinates in which the geodesic equations can be expressed simply, in terms of conserved quantities, without using explicitely initial conditions [4,5,7]. These results can be generalized easily to any dimensions by using the same type of static charts.…”

“…This paper is a technical piece of work whose principal purpose was to find new general results concerning the classical motion on hyperbolic spactimes of any dimensions. The generalization of the geodesic equations expressed in terms of conserved quantities, from d = 3 [7,5] to any dimensions, is somewhat natural since we used Cartesian coordinates. Nevertheless, our method of exploiting conserved quantities was more productive in studying the Boltzmann equation allowing us to derive the general form of the distributions of the Boltzmann-Marle model on the dS and AdS spacetimes of any dimensions.…”

“…The (1 + 3)-dimensional hyperbolic manifolds, the de Sitter (dS) and antide Sitter (AdS) spacetimes, are interesting because of their isometries which generate a large collection of conserved quantities which may be used for studying classical systems on these manifolds [1,2,3,4,5,6,7].…”

Light from Schwarzschild black holes in de Sitter expanding universe

“…The conserved quantities with physical meaning are the energy E, momentum P, angular momentum L and a specific vector Q that we call the adjoint momentum [49]. A geodesic in the co-moving frame {t, x} [59],…”