The Cauchy Problem for the Einstein Equations

TL;DR

This paper surveys the Cauchy problem for Einstein equations, focusing on local solutions, hyperbolic reductions, and conceptual issues, including new results on hyperbolic systems and background from PDE theory.

Contribution

It provides a comprehensive overview of the Cauchy problem for Einstein equations with new insights into hyperbolic reductions and clarifies conceptual challenges.

Findings

New results on hyperbolic reductions of Einstein equations

Clarification of conceptual issues in the Cauchy problem

Detailed explanation of PDE background relevant to Einstein equations

Abstract

Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in this context. The question of producing reduced systems of equations which are hyperbolic is examined in detail and some new results on that subject are presented. Relevant background from the theory of partial differential equations is also explained at some length