Surveys in Differential Geometry

Volume 20 (2015)

Beginnings of the Cauchy problem for Einstein’s field equations

Pages: 1 – 16



Yvonne Choquet-Bruhat (Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France)


This is a brief account of results on the Cauchy problem for the Einstein equations starting with the early works of Darmois and Lichnerowicz and going up to the proofs of existence and uniqueness of solutions global in space and local in time, in Sobolev spaces, for the general equations either in vacuum or with classical sources.


Cauchy problem for einstein equations, einstein equations in vacuum and coupled to other fields, initial data, evolution, hyperbolic pde, adm, gravitational waves, causality, sobolev spaces

2010 Mathematics Subject Classification

35A01, 35L51, 35Q76, 83C05, 83C35

Full Text (PDF format)

Published 7 July 2015