Propagation of singularities on AdS spacetimes for general boundary conditions and the holographic Hadamard condition

2018/12/17 by Oran Gannot, Gannot, Oran, Michał Wrochna +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1812.06564

openalex publication_date 2018/12/17 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

We consider the Klein-Gordon equation on asymptotically anti-de Sitter spacetimes subject to Neumann or Robin (or Dirichlet) boundary conditions, and prove propagation of singularities along generalized broken bicharacteristics. The result is formulated in terms of conormal regularity relative to a twisted Sobolev space. We use this to show the uniqueness, modulo regularising terms, of parametrices with prescribed b-wavefront set. Furthermore, in the context of quantum fields, we show a similar result for two-point functions satisfying a holographic Hadamard condition on the b-wavefront set.

Cited by

• The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography
• The Hadamard parametrix on half-Minkowski with Robin boundary conditions: Fundamental solutions and Hadamard states
• Singularities of Dirac-Coulomb propagators

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