A New Formulation of General Relativity - Part II: Pre-Radar Charts and Generating Functions in Arbitrary Space-Times

TL;DR

This paper addresses the inverse problem in general relativity, exploring the conditions under which pre-radar charts can be defined in arbitrary space-times, providing local solutions and criteria for global solutions.

Contribution

It offers a local constructive method for defining pre-radar charts and establishes sufficient conditions for their global existence in arbitrary space-times.

Findings

Provided a local constructive solution for pre-radar charts.

Identified sufficient conditions for global solutions.

Advanced understanding of the inverse problem in general relativity.

Abstract

In this paper (Part II), the so-called inverse problem is treated. This means the question whether it is possible to define pre-radar charts, i.e. generating functions in arbitrary space-times. This problem is subtle. A local general constructive solution of it is presented. Sufficient conditions for the existence of global solutions are given.