The Chrono-Geometrical Structure of General Relativity and Clock Synchronization

TL;DR

This paper explores how in certain models of general relativity, the structure of space and clock synchronization are dynamically determined by Einstein's equations, impacting relativistic effects and precision timekeeping.

Contribution

It introduces a framework where the instantaneous 3-space and clock synchronization are derived from Einstein's equations in specific general relativity models.

Findings

The 3-space structure is dynamically determined in some models.

Implications for relativistic effects around Earth are analyzed.

Relevance for high-precision atomic clock metrology.

Abstract

After a review of the chrono-geometrical structure of special relativity, where the definition of the instantaneous 3-space is based on the observer-dependent convention for the synchronization of distant clocks, it is shown that in a class of models of general relativity the instantaneous 3-space and the associated clock synchronization convention are dynamically determined by Einstein's equations. This theoretical framework is necessary to understand the relativistic effects around the Earth, to be tested with the ACES mission of ESA, and the implications for metrology induced by the accuracy of the new generation of atomic clocks.