Dynamical and Hamiltonian formulation of General Relativity

TL;DR

This paper presents a Hamiltonian formulation of General Relativity, explaining its theoretical foundations and potential applications, aimed at making the complex reformulation accessible to graduate students.

Contribution

It provides a detailed, accessible reformulation of Einstein's equations as a Hamiltonian system, including technical and conceptual insights for the first time in a comprehensive manner.

Findings

Hamiltonian formulation of Einstein's equations introduced

Discussion of applications and conceptual aspects included

Self-contained presentation for graduate students provided

Abstract

This is a substantially expanded version of a chapter-contribution to "The Springer Handbook of Spacetime", edited by Abhay Ashtekar and Vesselin Petkov, published by Springer Verlag in 2014. This contribution introduces the reader to the reformulation of Einstein's field equations of General Relativity as a constrained evolutionary system of Hamiltonian type and discusses some of its uses, together with some technical and conceptual aspects. Attempts were made to keep the presentation self contained and accessible to first-year graduate students. This implies a certain degree of explicitness and occasional reviews of background material.