Coordinates and frames from the causal point of view

TL;DR

This paper explores the diverse causal classes of Lorentzian frames, highlighting their relevance in understanding and classifying various relativistic coordinate systems, including well-known and less familiar ones.

Contribution

It reveals the causal classes of several important coordinate systems and discusses their significance in the physical construction and classification of relativistic frames.

Findings

Identification of causal classes for Lemaître, Eddington-Finkelstein, and Bondi-Sachs coordinates.

Analysis of causal classes for Coll light and Coll positioning systems.

Emphasis on the role of causal classes in understanding relativistic coordinate systems.

Abstract

Lorentzian frames may belong to one of the 199 causal classes. Of these numerous causal classes, people are essentially aware only of two of them. Nevertheless, other causal classes are present in some well-known solutions, or present a strong interest in the physical construction of coordinate systems. Here we show the unusual causal classes to which belong so familiar coordinate systems as those of Lema{\^{\i}}tre, those of Eddington-Finkelstein, or those of Bondi-Sachs. Also the causal classes associated to the Coll light coordinates (four congruences of real geodetic null lines) and to the Coll positioning systems (light signals broadcasted by four clocks) are analyzed. The role that these results play in the comprehension and classification of relativistic coordinate systems is emphasized.