2002/05/06 by Eric Poisson
Physics and Astronomy · #Angular momentum #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Kerr metric #Linearized gravity #Mathematical physics #Minkowski space #Multipole expansion #Physics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Scalar field #Schwarzschild radius #Spacetime #Spacetime symmetries #Spherically symmetric spacetime #Stationary spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.66.044008
published as Phys.Rev. D66 (2002) 044008 · 17 pages, RevTeX4
arxiv created 2002/05/06 · openalex publication_date 2002/08/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed---the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically symmetric spacetime: it decays in time according to an inverse power law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.