On Breakdown Criteria for Nonvacuum Einstein Equations

Abstract

The recent "breakdown criterion" result of S. Klainerman and I. Rodnianski 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 author's Ph.D. thesis. In this paper, we state the main results of the thesis, 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.

62 pages This version: corrected minor typos, expanded Section 6 (geometry of null cones)

References in corpus (3)

• On Ricci coefficients of null hypersurfaces with time foliation in Einstein vacuum space-time
• A Generalized Representation Formula for Systems of Tensor Wave Equations
• An integral breakdown criterion for Einstein vacuum equations in the case of asymptotically flat spacetimes

Cited by in corpus (5)

• Rough sound waves in $3D$ compressible Euler flow with vorticity
• Unique continuation from infinity in asymptotically Anti-de Sitter spacetimes
• Non-existence of multiple-black-hole solutions close to Kerr-Newman
• On the Geometry of Null Cones to Infinity Under Curvature Flux Bounds
• New tensorial estimates in Besov spaces for time-dependent $(2+1)$-dimensional problems