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 (5)

• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• 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
• 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

Cited by in corpus (6)

• 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