Late-time tails of a self-gravitating massless scalar field, revisited

Abstract

We discuss the nonlinear origin of the power-law tail in the long-time evolution of a spherically symmetric self-gravitating massless scalar field in even-dimensional spacetimes. Using third-order perturbation method, we derive explicit expressions for the tail (the decay rate and the amplitude) for solutions starting from small initial data and we verify this prediction via numerical integration of the Einstein-scalar field equations in four and six dimensions. Our results show that the coincidence of decay rates of linear and nonlinear tails in four dimensions (which has misguided some tail hunters in the past) is in a sense accidental and does not hold in higher dimensions.

10 pages, 6 figures, one reference added, updated to conform with published version

References in corpus (7)

• A proof of Price's law for the collapse of a self-gravitating scalar field
• News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes
• On asymptotic stability of the Skyrmion
• Late-time tails of a Yang-Mills field on Minkowski and Schwarzschild backgrounds
• Linear and nonlinear tails II: exact decay rates in spherical symmetry
• Anomalously small wave tails in higher dimensions
• A note on late-time tails of spherical nonlinear waves

Cited by in corpus (14)

• Quasinormal modes of black holes: from astrophysics to string theory
• Asymptotics of Schwarzschild black hole perturbations
• Position space analysis of the AdS (in)stability problem
• Conditionally Extended Validity of Perturbation Theory: Persistence of AdS Stability Islands
• Hushing black holes: tails in dynamical spacetimes
• On the Relation Between Asymptotic Charges, the Failure of Peeling and Late-time Tails
• Late-time tails of wave maps coupled to gravity
• Quantitative decay rates for dispersive solutions to the Einstein-scalar field system in spherical symmetry
• Analytical and numerical treatment of perturbed black holes in horizon-penetrating coordinates
• A note about late-time wave tails on a dynamical background
• Dirac Fermions in Non-trivial Topology Black Hole Backgrounds
• Features of gravitational waves in higher dimensions
• Comment on "Late-time tails of a self-gravitating massless scalar field revisited" by Bizon et al: The leading order asymptotics
• Reply to the comment by Szpak on leading order asymptotics of late-time tails for a self-gravitating massless scalar field