Hidden symmetries and decay for the wave equation on the Kerr spacetime
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Publication:894308
DOI10.4007/annals.2015.182.3.1zbMath1373.35307arXiv0908.2265OpenAlexW2943994220MaRDI QIDQ894308
Publication date: 30 November 2015
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0908.2265
Relativistic cosmology (83F05) Black holes (83C57) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Einstein equations (35Q76)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Decay for solutions of the wave equation on Kerr exterior spacetimes. III: The full subextremalcase \(|a| < M\).
- Characterisation of the energy of Gaussian beams on Lorentzian manifolds: with applications to black hole spacetimes
- A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds
- On pointwise decay of linear waves on a Schwarzschild black hole background
- Cauchy problems for the conformal vacuum field equations in general relativity
- Conformal Killing tensors of order 2 for the Schwarzschild metric
- An integral spectral representation of the propagator for the wave equation in the Kerr geometry
- Strichartz estimates on Schwarzschild black hole backgrounds
- Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space
- Phase space analysis on some black hole manifolds
- Black hole physics. Basic concepts and new developments
- Decay rates and probability estimates for massive Dirac particles in the Kerr-Newman black hole geometry
- Spherical photon orbits around a Kerr black hole
- Global existence for the Einstein vacuum equations in wave coordinates
- A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating Kerr black hole
- A space-time integral estimate for a large data semi-linear wave equation on the Schwarzschild manifold
- Quantitative mode stability for the wave equation on the Kerr spacetime
- On quadratic first integrals of the geodesic equations for type [22 spacetimes]
- A proof of Price's law for the collapse of a self-gravitating scalar field
- Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior
- Mode stability of the Kerr black hole
- A new physical-space approach to decay for the wave equation with applications to black hole spacetimes
- A Local Energy Estimate on Kerr Black Hole Backgrounds
- Strichartz estimates on Kerr black hole backgrounds
- The decay of solutions of the exterior initial-boundary value problem for the wave equation
- Geometrical classification of Killing tensors on bidimensional flat manifolds
- DECAY OF THE MAXWELL FIELD ON THE SCHWARZSCHILD MANIFOLD
- The red‐shift effect and radiation decay on black hole spacetimes
- Uniform decay estimates and the lorentz invariance of the classical wave equation
- SCATTERING OF MASSLESS DIRAC FIELDS BY A KERR BLACK HOLE
- Sur la théorie de la diffusion pour l'équation de Klein–Gordon dans la métrique de Kerr
- Local decay of waves on asymptotically flat stationary space-times
- Lectures on black holes and linear waves
- A Decay Estimate for a Wave Equation with Trapping and a Complex Potential
- Global Structure of the Kerr Family of Gravitational Fields
- Solutions of the wave equation with localized energy
- General Relativity
- Uniqueness of smooth stationary black holes in vacuum: Small perturbations of the Kerr spaces
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