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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 explore the quantum nature of black holes by introducing an effective framework that takes into account deviations from the classical results. The approach is based on introducing quantum corrections to the classical Schwarzschild…

General Relativity and Quantum Cosmology · Physics 2022-09-14 Emanuele Binetti , Manuel Del Piano , Stefan Hohenegger , Franco Pezzella , Francesco Sannino

We present the first rigorous study of nonlinear wave equations on extremal black hole spacetimes without any symmetry assumptions on the solution. Specifically, we prove global existence with asymptotic blow-up for solutions to nonlinear…

Analysis of PDEs · Mathematics 2021-02-25 Yannis Angelopoulos , Stefanos Aretakis , Dejan Gajic

We develop a novel technique through spectral decompositions to study the gravitational perturbations of a black hole, without needing to decouple the linearized field equations into master equations and separate their radial and angular…

General Relativity and Quantum Cosmology · Physics 2023-06-19 Adrian Ka-Wai Chung , Pratik Wagle , Nicolas Yunes

We study axisymmetric solution to the conformally invariant wave equation on a Kerr background by means of numerical and analytical methods. Our main focus is on the behaviour of the solutions near spacelike infinity, which is appropriately…

General Relativity and Quantum Cosmology · Physics 2021-06-07 Jörg Hennig , Rodrigo Panosso Macedo

In this study, the gravitational decoupling approach via extended geometric deformation is utilized to generate analytical black hole solutions owing to its simplicity and effectiveness. Considering the external fields surrounding…

General Relativity and Quantum Cosmology · Physics 2022-12-12 Chao-Ming Zhang , Ming Zhang , De-Cheng Zou

We investigate several aspects of exact black hole solutions in asymptotically Lifshitz spacetime, which were proposed in 0812.0530. Firstly, we calculate the tidal forces and find that in the near horizon region of such black hole…

High Energy Physics - Theory · Physics 2009-11-14 Da-Wei Pang

We study axial gravitational perturbations of a hairy black hole constructed in the framework of gravitational decoupling and investigate the geometric origin of echo-like late-time signals in this spacetime. We derive the odd-parity master…

General Relativity and Quantum Cosmology · Physics 2026-04-09 Yi Yang , Ali Ovgun , Gaetano Lambiase , Dong Liu , Zheng-Wen Long

We study the behaviour of smooth solutions to the wave equation, $\square_g\psi=0$, in the interior of a fixed Schwarzschild black hole. In particular, we obtain a full asymptotic expansion for all solutions towards $r=0$ and show that it…

General Relativity and Quantum Cosmology · Physics 2019-09-04 Grigorios Fournodavlos , Jan Sbierski

We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…

Numerical Analysis · Mathematics 2014-02-24 Terry Haut , Beth Wingate

We consider a broad class of static, spherically symmetric generalized Schwarzschild-like solutions with multiple non-interacting anisotropic fluid sources and derive the coordinate transformation from Schwarzschild-like (curvature) to…

General Relativity and Quantum Cosmology · Physics 2026-03-24 Zeyu Zeng , Elena Kopteva

We study asymptotics for solutions of Maxwell's equations, in fact of the Hodge-de Rham equation $(d+\delta)u=0$ without restriction on the form degree, on a geometric class of stationary spacetimes with a warped product type structure…

Analysis of PDEs · Mathematics 2020-05-28 Peter Hintz , Andras Vasy

We present a new general method for proving global decay of energy through a suitable spacetime foliation, as well as pointwise decay, starting from an integrated local energy decay estimate. The method is quite robust, requiring only…

Analysis of PDEs · Mathematics 2025-09-30 Mihalis Dafermos , Igor Rodnianski

In this paper, we derive the early-time asymptotics for fixed-frequency solutions $\phi_\ell$ to the wave equation $\Box_g \phi_\ell=0$ on a fixed Schwarzschild background ($M>0$) arising from the no incoming radiation condition on…

General Relativity and Quantum Cosmology · Physics 2025-08-20 Lionor M. A. Kehrberger

We consider solutions to the linear wave equation in the interior region of extremal Kerr black holes. We show that axisymmetric solutions can be extended continuously beyond the Cauchy horizon and moreover that, if we assume suitably fast…

General Relativity and Quantum Cosmology · Physics 2015-12-31 Dejan Gajic

The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrodinger-like equation to the complex plane and then performing a method of monodromy matching at the…

High Energy Physics - Theory · Physics 2015-06-26 Vitor Cardoso , Jose Natario , Ricardo Schiappa

We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Luis Lehner

We give asymptotics for Einstein vacuum equations in wave coordinates with small asymptotically flat data. We show that the behavior is wave like at null infinity and homogeneous towards time like infinity. We use the asymptotics to show…

Analysis of PDEs · Mathematics 2017-04-26 Hans Lindblad

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

We study analytically the asymptotic late-time evolution of realistic rotating collapse. This is done by considering the asymptotic late-time solutions of Teukolsky's master equation, which governs the evolution of gravitational,…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Shahar Hod