Gravitational clock compass in General Relativity

TL;DR

This paper introduces a method using a set of clocks, called a clock compass, to determine all components of the gravitational field in General Relativity, with applications in relativistic geodesy.

Contribution

It presents a novel approach to measure the gravitational field using clocks, contrasting with traditional methods based on test body accelerations.

Findings

Clock compass can determine all gravitational field components.

Constructs a reference frame for gravitational measurements.

Applicable to relativistic geodesy networks.

Abstract

We show how a suitably prepared set of clocks can be used to determine all components of the gravitational field in General Relativity. We call such an experimental setup a clock compass, in analogy to the usual gravitational compass. Particular attention is paid to the construction of the underlying reference frame. Conceptual differences between the clock compass and the standard gravitational compass, which is based on the measurement of the mutual accelerations between the constituents of a swarm of test bodies, are highlighted. Our results are of direct operational relevance for the setup of networks of clocks, for example in the context of relativistic geodesy.