A Vector Field Method Approach to Improved Decay for Solutions to the\n Wave Equation on a Slowly Rotating Kerr Black Hole

2010/09/03 by Jonathan Luk, Luk, Jonathan
Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Pulsars and Gravitational Waves Research

paper · pdf · doi:10.48550/arxiv.1009.0671

openalex publication_date 2010/09/03 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We prove that sufficiently regular solutions to the wave equation\n Box_gK\Φ=0 on the exterior of a sufficiently slowly rotating Kerr black\nhole obey the estimates |\Φ|\≤ C (t^*)^-3/2+\η on a compact region of\nr. This is proved with the help of a new vector field commutator that is\nanalogous to the scaling vector field on Minkowski and Schwarzschild spacetime.\nThis result improves the known robust decay rates that are proved using the\nvector field method in the region of finite r and along the event horizon.\n

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