Price's law for spin fields on a Schwarzschild background

Abstract

In this work, we derive the globally precise late-time asymptotics for the spin-$\mathfrak{s}$ fields on a Schwarzschild background, including the scalar field $(\mathfrak{s}=0)$, the Maxwell field $(\mathfrak{s}=\pm 1)$ and the linearized gravity $(\mathfrak{s}=\pm 2)$. The conjectured Price's law in the physics literature which predicts the sharp rates of decay of the spin $s=\pm \mathfrak{s}$ components towards the future null infinity as well as in a compact region is shown. Further, we confirm the heuristic claim by Barack and Ori that the spin $+1,+2$ components have an extra power of decay at the event horizon than the conjectured Price's law. The asymptotics are derived via a unified, detailed analysis of the Teukolsky master equation that is satisfied by all these components.

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References in corpus (35)

• 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
• Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space
• Decay of Solutions of the Wave Equation in the Kerr Geometry
• Strichartz estimates on Schwarzschild black hole backgrounds
• A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
• Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime
• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• Mode-Coupling in Rotating Gravitational Collapse of a Scalar Field
• Late time tails in the Kerr spacetime
• Late-time asymptotics for the wave equation on extremal Reissner-Nordström backgrounds
• New identities for linearized gravity on the Kerr spacetime
• 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
• Mode stability for the Teukolsky equation on extremal and subextremal Kerr spacetimes
• 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
• The linear stability of Reissner-Nordström spacetime for small charge
• Linear Stability of Schwarzschild Spacetime: Decay of Metric Coefficients
• 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
• Sharp decay estimates for massless Dirac fields on a Schwarzschild background
• Price's law and precise late-time asymptotics for subextremal Reissner-Nordström black holes
• Numerical investigation of the dynamics of linear spin $s$ fields on Kerr background I. Late time tails of spin $s=\pm 1,\pm 2$ fields
• Comments on tails in Schwarzschild spacetimes
• A space-time integral estimate for a large data semi-linear wave equation on the Schwarzschild manifold
• Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field
• A Positive-Definite Energy Functional for Axially Symmetric Maxwell's Equations on Kerr-de Sitter Black Hole Spacetimes
• A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes

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• On the Relation Between Asymptotic Charges, the Failure of Peeling and Late-time Tails
• The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher $\ell$-Modes of Linear Waves on a Schwarzschild Background
• The Case Against Smooth Null Infinity II: A Logarithmically Modified Price's Law
• The Case Against Smooth Null Infinity IV: Linearised Gravity Around Schwarzschild -- An Overview
• Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
• The Case Against Smooth Null Infinity V: Early-Time Asymptotics of Linearised Gravity Around Schwarzschild for Fixed Spherical Harmonic Modes