PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION

DOI10.1017/S147474802000002XzbMath1503.81024arXiv1812.06564OpenAlexW2904565886MaRDI QIDQ5023830

Oran Gannot, Michał Wrochna

Publication date: 25 January 2022

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.06564

zbMATH Keywords

Klein-Gordon equationHadamard statespropagation of singularitiesquantum field theory on curved spacetimesanti-de Sitter spacetimes

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum field theory on curved space or space-time backgrounds (81T20) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Asymptotic procedures (radiation, news functions, (mathcal{H} )-spaces, etc.) in general relativity and gravitational theory (83C30) Propagation of singularities; initial value problems on manifolds (58J47) Wave front sets in context of PDEs (35A18) Boolean and Hadamard matrices (15B34)

Related Items

On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary ⋮ A generalization of the propagation of singularities theorem on asymptotically anti‐de Sitter spacetimes ⋮ Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions ⋮ Boundary conditions and infrared divergences ⋮ Møller operators and Hadamard states for Dirac fields with MIT boundary conditions ⋮ Diophantine approximation as cosmic censor for Kerr-AdS black holes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unique continuation from infinity in asymptotically anti-de Sitter spacetimes
• The massive wave equation in asymptotically AdS spacetimes
• Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry
• Fractional Laplacian in conformal geometry
• The Klein-Gordon equation in the anti-de Sitter cosmology
• Propagation of singularities for the wave equation on edge manifolds
• Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime
• Stability in gauged extended supergravity
• Transformation of boundary problems
• Einstein metrics with prescribed conformal infinity on the ball
• The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes
• A singular initial-boundary value problem for nonlinear wave equations and holography in asymptotically anti-de Sitter spaces
• Micro-local approach to the Hadamard condition in quantum field theory on curved space-time
• The wave equation on asymptotically anti de Sitter spaces
• Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes
• Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary
• Fractional powers of the wave operator via Dirichlet-to-Neumann maps in anti-de Sitter spaces
• A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem
• Propagation of singularities for the wave equation on manifolds with corners
• The global rotating scalar field vacuum on anti-de Sitter spacetime
• Fractional conformal Laplacians and fractional Yamabe problems
• Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes
• On quasinormal modes of asymptotically anti-de Sitter black holes
• Fourier integral operators. II
• Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds
• Decay Properties of Klein-Gordon Fields on Kerr-AdS Spacetimes
• WELL-POSEDNESS FOR THE MASSIVE WAVE EQUATION ON ASYMPTOTICALLY ANTI-DE SITTER SPACETIMES
• Singularities of boundary value problems. II
• Elliptic theory of differential edge operators I
• Grazing rays and reflection of singularities of solutions to wave equations
• Singularities of boundary value problems. I
• Propagation des ondes dans les variétés à coins
• On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime
• Unique continuation from infinity in asymptotically anti-de Sitter spacetimes II: Non-static boundaries
• A Simple Diffractive Boundary Value Problem on an Asymptotically Anti-de Sitter Space
• Diffraction at Corners for the Wave Equation on Differential Forms
• A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes
• Elliptic theory of differential edge operators II: boundary value problems

This page was built for publication: PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION