2 Local Existence 

In this section basic facts about local existence theorems for the Einstein equations are recalled. Since the theory is well developed and good accounts exist elsewhere (see for instance [108]), attention is focussed on remaining open questions known to the author. In particular, the questions of the minimal regularity required to get a well-posed problem and of free boundaries for fluid bodies are discussed.

• 2.1 The constraints
• 2.2 The vacuum evolution equations
• 2.3 Questions of differentiability
• 2.4 New techniques for rough solutions
• 2.5 Matter fields
• 2.6 Free boundary problems

Theorems on Existence and Global Dynamics for the Einstein Equations Alan D. Rendall http://www.livingreviews.org/lrr-2002-6 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de