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For any sub-extremal Kerr spacetime with non-zero angular momentum, we find an open family of non-zero masses for which there exist smooth, finite energy, and exponentially growing solutions to the corresponding Klein-Gordon equation. If…

General Relativity and Quantum Cosmology · Physics 2015-11-10 Yakov Shlapentokh-Rothman

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…

Analysis of PDEs · Mathematics 2019-11-12 Elek Csobo , François Genoud , Masahito Ohta , Julien Royer

The Hyperboloidal Foliation Method (introduced by the authors in 2014) is extended here and applied to the Einstein equations of general relativity. Specifically, we establish the nonlinear stability of Minkowski spacetime for…

Analysis of PDEs · Mathematics 2016-01-27 Philippe G. LeFloch , Yue Ma

We are interested in the stability of a class of totally geodesic wave maps, as recently studied by Abbrescia and Chen, and later by Duan and Ma. The relevant equations of motion are a system of coupled semilinear wave and Klein-Gordon…

Analysis of PDEs · Mathematics 2023-11-15 Shijie Dong , Zoe Wyatt

We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an…

Mathematical Physics · Physics 2024-06-18 Ernesto Nungesser

This is a first in a series of papers in which we study the stability of the $(1+n)$-Minkowski space-time, for $n \geq 3$, solution to the Einstein-Yang-Mills equations, in both the Lorenz and harmonic gauges, associated to any arbitrary…

Analysis of PDEs · Mathematics 2023-10-13 Sari Ghanem

We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an $n-$manifold of…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Gustavo Dotti , Reinaldo J. Gleiser

We prove the exterior stability of the Minkowski space-time, $\mathbb{R}^{1+3}$, solution to the Einstein-Yang-Mills system in both the Lorenz and harmonic gauges, where the Yang-Mills fields are valued in any arbitrary Lie algebra…

Analysis of PDEs · Mathematics 2023-10-13 Sari Ghanem

We study the black ring solution in the Einstein-Gauss-Bonnet (EGB) theory at large $D$. By using the $1/D$ expansion in the near horizon region we derive the effective equations for the slowly rotating black holes in the EGB theory. The…

High Energy Physics - Theory · Physics 2018-08-01 Bin Chen , Peng-Cheng Li , Cheng-Yong Zhang

We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1+3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an…

General Relativity and Quantum Cosmology · Physics 2018-08-29 Kyriakos Destounis , Grigoris Panotopoulos , Ángel Rincon

In this paper we show the classical global stability of the flat Kaluza-Klein spacetime, which corresponds to Minkowski spacetime in $\m R^{1+4}$ with one direction compactified on a circle. We consider small perturbations which are allowed…

General Relativity and Quantum Cosmology · Physics 2023-07-31 Cécile Huneau , Annalaura Stingo , Zoe Wyatt

We derive master equations for linear perturbations in Einstein-Maxwell-scalar theory, for any spacetime dimension D and any background with a maximally symmetric n = (D - 2)-dimensional spatial component. This is done by expressing all…

High Energy Physics - Theory · Physics 2021-04-23 Aron Jansen , Andrzej Rostworowski , Mieszko Rutkowski

We study small perturbations of the well-known family of Friedman-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions to the dust-Einstein system with a positive cosmological constant in the case that the spacelike Cauchy hypersurfaces are…

Analysis of PDEs · Mathematics 2013-11-07 Mahir Hadzic , Jared Speck

We incorporate a massless scalar field into a 3-dimensional code for the characteristic evolution of the gravitational field. The extended 3-dimensional code for the Einstein--Klein--Gordon system is calibrated to be second order…

General Relativity and Quantum Cosmology · Physics 2008-11-26 W. Barreto , A. Da Silva , R. Gomez , L. Lehner , L. Rosales , J. Winicour

In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to first and third harmonics, which leads to a reduced partial…

Pattern Formation and Solitons · Physics 2025-08-19 A. G. Stefanov , M. Stanislavova , J. Cuevas-Maraver , P. G. Kevrekidis

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon…

General Relativity and Quantum Cosmology · Physics 2012-11-20 Horst Reinhard Beyer , Miguel Alcubierre , Miguel Megevand , Juan Carlos Degollado

We prove nonlinear Lyapunov stability of a family of `$n+1$'-dimensional cosmological models of general relativity locally isometric to the Friedman Lema\^itre Robertson Walker (FLRW) spacetimes including a positive cosmological constant.…

General Relativity and Quantum Cosmology · Physics 2022-03-31 Puskar Mondal

This note complements the paper \cite{LP} by proving a scattering statement for solutions of nonlinear Klein-Gordon equations with an internal mode in $3$d. We show that small solutions exhibit growth around a one-dimensional set in…

Analysis of PDEs · Mathematics 2022-03-14 Tristan Léger , Fabio Pusateri

In this paper, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordstr\"om family of charged black holes with small charge. Solutions to the linearized Einstein-Maxwell equations around a…

General Relativity and Quantum Cosmology · Physics 2020-09-03 Elena Giorgi

This paper establishes the global existence of solutions for a class of wave-Klein-Gordon coupled systems with specific nonlinearities in 3+1-dimensional Minkowski spacetime. The study demonstrates that imposing certain constraints on the…

Analysis of PDEs · Mathematics 2026-04-21 Yue Ma , Weidong Zhang