A Generalized Representation Formula for Systems of Tensor Wave Equations

Abstract

In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better highlights that such representation formulas are supported entirely on past null cones. This generalization is a key component for extending Klainerman and Rodnianski's breakdown criterion result for Einstein-vacuum spacetimes to Einstein-Maxwell and Einstein-Yang-Mills spacetimes.

29 pages

Cited by in corpus (5)

• Unique continuation from infinity in asymptotically Anti-de Sitter spacetimes
• On Breakdown Criteria for Nonvacuum Einstein Equations
• Null Geodesics and Improved Unique Continuation for Waves in Asymptotically Anti-de Sitter Spacetimes
• The bulk-boundary correspondence for the Einstein equations in asymptotically Anti-de Sitter spacetimes
• New tensorial estimates in Besov spaces for time-dependent $(2+1)$-dimensional problems