A null frame for spacetime positioning by means of pulsating sources

TL;DR

This paper proposes a relativistic positioning system using pulsating sources like pulsars, employing null four-vectors in flat spacetime to determine user coordinates and trajectories.

Contribution

It introduces an operational framework for spacetime positioning with pulsating sources at infinity, utilizing null bases in flat spacetime, and demonstrates its application with pulsars.

Findings

Pulsar signals can define a relativistic positioning system.

User coordinates and trajectories can be determined from pulse reception.

The approach is valid in flat Minkowski spacetime.

Abstract

We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of four-dimensional bases of null four-vectors, in flat spacetime. As a prototypical case, we show how pulsars can be used to define such a positioning system. The reception of the pulses for a set of different sources whose positions in the sky and periods are assumed to be known allows the determination of the user's coordinates and spacetime trajectory, in the reference frame where the sources are at rest. We describe our approach in flat Minkowski spacetime, and discuss the validity of this and other approximations we have considered.