Rest frames and relativistic effects on de Sitter spacetimes

Abstract

It is shown that the Nachtmann boosting method of introducing coordinates on de Sitter manifolds can be completed with suitable gauge transformations able to keep under control the transformation under isometries of the conserved quantities. With this method, the rest local charts (or natural frames) are defined pointing out the role of the conserved quantities in investigating the relative geodesic motion. The advantages of this approach can be seen from the applications presented here. For the first time, the simple kinematic effects, the electromagnetic field of a free falling charge and the binary fission are solved in terms of conserved quantities on the expanding portion of the de Sitter spacetime.

de Sitter relativity in static charts

“…The conserved quantities with physical meaning [6][7][8]10] are the well-known energy and angular momentum,…”

“…On the contrary, in the comoving local charts we used so far (i.e. the conformal Euclidean and de Sitter-Painlevé ones), the dS relativity seems to be closer to the Einstein special relativity since here we have translations and conserved momenta such that at least in the conformal Euclidean chart all the geodesic trajectories are rectilinear along the momentum direction [6,10].…”

“…All these spacetimes have highest possible isometries [2] representing thus a good framework for studying the role of the conserved quantities with physical meaning in quantum theory [3][4][5][6] or for describing the classical relative geodesic motion [7][8][9]. With their help we constructed recently the dS relativity [10] in comoving charts [11] and the AdS relativity [12] in static and spherically symmetric local charts that complete our image of the special relativity in spacetimes with maximal symmetry.…”

“…The conserved quantities on these geodesics help us to mark the different inertial frames whose relative motion can then be studied by using the Nachtmann boosting method a e-mail: i.cotaescu@e-uvt.ro of introducing coordinates in different dS local charts [3]. In this manner, we derived the Lorentzian isometries relating the coordinates of the moving and fixed inertial frames on dS or AdS backgrounds [10,12].…”

“…[10] since then we can take over the results obtained therein without revisiting the entire boosting method which allowed us to construct the dS and AdS relativity. In this manner we obtain a version of the dS relativity in static charts which is perfectly symmetric with the AdS one with respect to the change of the hyperbolic functions into trigonometric ones.…”