Sharp decay estimates for massless Dirac fields on a Schwarzschild background

Abstract

We consider the explicit asymptotic profile of massless Dirac fields on a Schwarzschild background. First, we prove for the spin $s=\pm \frac{1}{2}$ components of the Dirac field a uniform bound of a positive definite energy and an integrated local energy decay estimate from a symmetric hyperbolic wave system. Based on these estimates, we further show that these components have globally pointwise decay $f{v}^{-3/2-s}{\tau }^{-5/2+s}$ as both an upper and a lower bound outside the black hole, with function $f$ finite and explicitly expressed in terms of the initial data and the coordinates. This establishes the validity of the conjectured Price's law for massless Dirac fields outside a Schwarzschild black hole.

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References in corpus (32)

• The linear stability of the Schwarzschild solution to gravitational perturbations
• A new physical-space approach to decay for the wave equation with applications to black hole spacetimes
• The black hole stability problem for linear scalar perturbations
• The global non-linear stability of the Kerr-de Sitter family of black holes
• A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds
• Strichartz estimates on Schwarzschild black hole backgrounds
• A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• The Long-Time Dynamics of Dirac Particles in the Kerr-Newman Black Hole Geometry
• Decay Rates and Probability Estimates for Massive Dirac Particles in the Kerr-Newman Black Hole Geometry
• Decay of linear waves on higher dimensional Schwarzschild black holes
• Late time tails from momentarily stationary, compact initial data in Schwarzschild spacetimes
• Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: linearized gravity
• Late-time decay of gravitational and electromagnetic perturbations along the event horizon
• The linear stability of Reissner-Nordström spacetime: the full subextremal range
• Pointwise decay for the Maxwell field on black hole space-times
• The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge
• Linear Stability of the Non-Extreme Kerr Black Hole
• Decay of solutions to the Maxwell equation on the Schwarzschild background
• A sharp version of Price's law for wave decay on asymptotically flat spacetimes
• Peeling of Dirac and Maxwell fields on a Schwarzschild background
• Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole I: Maxwell field
• Linear Stability of Schwarzschild Spacetime: Decay of Metric Coefficients
• The Massive Dirac Equation in the Kerr Geometry: Separability in Eddington-Finkelstein-type Coordinates and Asymptotics
• Scattering for massive Dirac fields on the Kerr metric
• A space-time integral estimate for a large data semi-linear wave equation on the Schwarzschild manifold
• Asymptotic Behavior of Massless Dirac Waves in Schwarzschild geometry
• Peeling on Kerr spacetime~:linear and non linear scalar fields
• Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field
• Peeling of Dirac fields on Kerr spacetimes
• A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes
• Scattering theory for Dirac fields inside a Reissner-Nordström-type black hole

Cited by in corpus (6)

• Eigenvalue repulsions and quasinormal mode spectra of Kerr-Newman: an extended study
• Price's law and precise late-time asymptotics for subextremal Reissner-Nordström black holes
• Price's law for spin fields on a Schwarzschild background
• The characteristic gluing problem for the Einstein equations and applications
• Conformal scattering theory for the Dirac field on Kerr spacetime
• Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime