caa a22 4500 445320559 CHVBK 20180317142702.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00023-011-0082-7 doi (NATIONALLICENCE)springer-10.1007/s00023-011-0082-7 Shao Arick Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA aut On Breakdown Criteria for Nonvacuum Einstein Equations [Elektronische Daten] [Arick Shao] The recent "breakdown criterion” result of Klainerman and Rodnianski (On the breakdown criterion in general relativity, Preprint, 2009) stated roughly that an Einstein-vacuum spacetime, given as a CMC foliation, can be further extended in time if the second fundamental form and the derivative of the lapse of the foliation are uniformly bounded. This theorem and its proof were extended to Einstein-scalar and Einstein-Maxwell spacetimes in the thesis (Shao in Breakdown criteria for nonvacuum Einstein equations, Ph.D. thesis, Princeton University, 2010). In this paper, we state the main results of Shao (2010), and we summarize and discuss their proofs. In particular, we will discuss the various issues resulting from nontrivial Ricci curvature and the coupling between the Einstein and the field equations. Springer Basel AG, 2011 Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/2(2011-03-01), 205-277 1424-0637 12:2<205 2011 12 23 https://doi.org/10.1007/s00023-011-0082-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-011-0082-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Shao Arick Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/2(2011-03-01), 205-277 1424-0637 12:2<205 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer