Equivalent Generic Forms for Metric Fields Yielded by Relativistic Positioning Systems

TL;DR

This paper demonstrates that any Lorentzian metric in relativistic positioning systems can be transformed into a generic form using only four positive functions, simplifying the analysis of such systems.

Contribution

It introduces a method to represent Lorentzian metrics in a simplified, generic form within relativistic positioning systems, enhancing understanding and potential applications.

Findings

Any Lorentzian metric in $\u007bell$-frames is isometrically equivalent to a generic metric.

The generic metric depends on only four positive functions.

This representation simplifies the analysis of relativistic positioning systems.

Abstract

Relativistic positioning systems provide tensors represented in $\{\ell\ell\ell\ell\}$-frames ($\ell$ for light) dual to systems of emission coordinates. We show that any Lorentzian metric field given in such a frame is isometrically equivalent to a generic metric field defined by only four positive functions depending on another specific system of emission coordinates.