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We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the…

General Relativity and Quantum Cosmology · Physics 2010-11-19 Lior M. Burko , Amos Ori

The late-time tail behavior of massive scalar fields is studied analytically in a stationary axisymmetric EMDA black hole geometry. It is shown that the asymptotic behavior of massive perturbations is dominated by the oscillatory inverse…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Qiyuan Pan , Jiliang Jing

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.

Mathematical Physics · Physics 2011-03-23 Nikodem Szpak , Piotr Bizoń , Tadeusz Chmaj , Andrzej Rostworowski

We investigate the late-time behavior of the massive vector field in the background of the Schwarzschild and Schwarzschild-de Sitter black holes. For Schwarzschild black hole, at intermediately late times the massive vector field is…

General Relativity and Quantum Cosmology · Physics 2008-11-26 R. A. Konoplya , C. Molina , A. Zhidenko

The late-time tail behaviors of massive scalar fields are examined analytically in the background of a black hole with a global monopole. It is found that the presence of a solid deficit angle in the background metric makes the massive…

General Relativity and Quantum Cosmology · Physics 2011-08-11 Hongwei Yu

This is the second part of a series of papers deriving the precise, late-time behaviour and (in)stability properties of charged scalar fields on near-extremal Reissner--Nordstr\"om spacetimes via energy estimates. In this paper, we use…

General Relativity and Quantum Cosmology · Physics 2026-04-01 Dejan Gajic

It was first pointed out by Koyama and Tomimatsu that, under reasonable assumptions, the asymptotic late-time tails of massive scalar perturbations in the far zone of spherically symmetric black hole spacetimes decays universally as…

General Relativity and Quantum Cosmology · Physics 2022-10-18 Wei-Liang Qian , Kai Lin , Cai-Ying Shao , Bin Wang , Rui-Hong Yue

We present a comprehensive analysis of late-time tails in gravitational radiation from merging spin-aligned eccentric binary black holes, using high-accuracy point-particle black hole perturbation theory simulations. We simulate the…

General Relativity and Quantum Cosmology · Physics 2025-12-01 Tousif Islam , Guglielmo Faggioli , Gaurav Khanna

We invesigate analytically both the intermediate and late-time behaviour of the massive scalar field in the background of static spherically symmetric black hole solution in dilaton gravity with arbitrary coupling constant. The intermediate…

High Energy Physics - Theory · Physics 2008-11-26 Marek Rogatko

We consider a class of time dependent finite energy multi-soliton solutions of the U(N) integrable chiral model in $(2+1)$ dimensions. The corresponding extended solutions of the associated linear problem have a pole with arbitrary…

High Energy Physics - Theory · Physics 2008-11-26 Maciej Dunajski , Prim Plansangkate

We apply a new analytic scheme, developed in a preceding paper, in order to calculate the late time behavior of scalar test fields evolving outside a Schwarzschild black hole. The pattern of the late time decay at future null infinity is…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Leor Barack

Nonlinear tails in black hole perturbations, arising from second-order effects, present a distinct departure from the well-known Price tail of linear theory. We present an analytical derivation of the power law indices and amplitudes for…

General Relativity and Quantum Cosmology · Physics 2025-07-08 Siyang Ling , Sabeela Shah , Sam S. C. Wong

We examine perturbations of a massive scalar field around spherically symmetric, brane-localized black holes. Although the ringdown and asymptotic tails of various brane-world black holes have been extensively studied, there has been no…

General Relativity and Quantum Cosmology · Physics 2024-09-17 Alexey Dubinsky

We investigate dominant late-time tail behaviors of massive scalar fields in nearly extreme Reissner-Nordstr\"{o}m background. It is shown that the oscillatory tail of the scalar fields has the decay rate of $t^{-5/6}$ at asymptotically…

General Relativity and Quantum Cosmology · Physics 2007-10-02 Hiroko Koyama , Akira Tomimatsu

Schwarzschild black holes evolve toward their static configuration by emitting gravitational waves, which decay over time following a power law at fixed spatial positions. We derive this power law analytically for the second-order even…

General Relativity and Quantum Cosmology · Physics 2025-04-09 Alex Kehagias , Antonio Riotto

It is well known that the late-time behaviour of gravitational collapse is {\it dominated} by an inverse power-law decaying tail. We calculate {\it higher-order corrections} to this power-law behaviour in a spherically symmetric…

General Relativity and Quantum Cosmology · Physics 2010-11-19 Shahar Hod

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…

Statistics Theory · Mathematics 2013-12-20 J. L. Wadsworth , J. A. Tawn

Nonlinear effects play a fundamental role in the late-time ringdown of black holes, with direct implications for gravitational-wave observations. For massive fields, these dynamics become richer, yet their nonlinear signatures remain poorly…

General Relativity and Quantum Cosmology · Physics 2026-04-14 Caiying Shao , Zhen-Tao He , Jiageng Jiao , Jingqi Lai , Jun-Xi Shi , Yu Tian , Dandan Yuan , Hongbao Zhang

The late-time evolution of the charged massive Dirac fields in the background of a Reissner-Norstr\"om (RN) black hole is studied. It is found that the intermediate late-time behavior is dominated by an inverse power-law decaying tail…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Jiliang Jing

The need for more and more accurate gravitational wave templates requires taking into account all possible contributions to the emission of gravitational radiation from a binary system. Therefore, working within a…

General Relativity and Quantum Cosmology · Physics 2022-03-17 Donato Bini , Andrea Geralico