Institutionen för Matematik - KTH

• The introductory material (putting the Cauchy problem into a historical context), as well as a sketch of the proof of local existence is to be found in
  The Cauchy problem in general relativity. Acta Phys. Polon. B 44 (2013), no. 12, 2621--2641.
  A preprint version is to be found here.


• Some of the ODE material is to be found in my notes on Non-linear wave equations.


• A sketch of a proof of future global non-linear stability in a cosmological setting can be found here.


• A more extensive sketch of a proof of local existence can be found in Chapter 2 of the book
  Ringström, Hans On the topology and future stability of the universe. Oxford Mathematical Monographs. Oxford University Press, Oxford, 2013. xiv+718 pp. ISBN: 978-0-19-968029-0
  Moreover, that book contains a proof of local existence of solutions in the Einstein-Vlasov setting.


• For a proof of local existence of solutions in the vacuum setting, one reference is
  Ringström, Hans The Cauchy problem in general relativity. ESI Lectures in Mathematics and Physics. European Mathematical Society (EMS), Zürich, 2009. xiv+294 pp. ISBN: 978-3-03719-053-1


• Concerning the existence of a maximal globally hyperbolic development, one proof can be found here.