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We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation…

General Relativity and Quantum Cosmology · Physics 2022-12-29 Philippe G. LeFloch , Filipe C. Mena , The-Cang Nguyen

In this paper, we establish the global existence of a semi-linear class of hyperbolic equations in 3+1 dimensions, that satisfy the bounded weak null condition. We propose a conformal compactification of the future directed null-cone in…

Analysis of PDEs · Mathematics 2025-01-31 J. Arturo Olvera-Santamaria

We prove a large-data semi-global existence theorem and the dynamical formation of trapped surfaces for the Einstein-massless Vlasov system in 3+1 dimensions, without any symmetry assumptions. The analysis critically hinges on a finely…

Analysis of PDEs · Mathematics 2025-10-15 Nikolaos Athanasiou , Puskar Mondal , Shing-Tung Yau

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Alan D. Rendall

We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are…

General Relativity and Quantum Cosmology · Physics 2012-06-22 Christian G. Boehmer , Lukas Hollenstein , Francisco S. N. Lobo

We study the Einstein-Lichnerowicz constraints system, obtained through the conformal method when addressing the initial data problem for the Einstein equations in a scalar field theory. We prove that this system is stable with respect to…

Analysis of PDEs · Mathematics 2014-05-26 Olivier Druet , Bruno Premoselli

We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular…

General Relativity and Quantum Cosmology · Physics 2019-08-27 Mihalis Dafermos , Gustav Holzegel , Igor Rodnianski

In the Einstein gravity, it is well-known that strictly stationary and vacuum regular spacetime should be the Minkowski spacetime. In the Einstein-Gauss-Bonnet theory, we shall show the similar statement, that is, strictly static(no event…

General Relativity and Quantum Cosmology · Physics 2015-10-30 Tetsuya Shiromizu , Seiju Ohashi

In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…

General Relativity and Quantum Cosmology · Physics 2025-07-14 Thomas Mädler , Emanuel Gallo

We show that in four or more spacetime dimensions, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime for…

High Energy Physics - Theory · Physics 2009-11-10 Hideo Kodama , Akihiro Ishibashi

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…

General Relativity and Quantum Cosmology · Physics 2008-11-26 J. A. Cabezas , J. Martin-Martin , A. Molina , E. Ruiz

We present a general construction of semiglobal scattering solutions to quasilinear wave equations in a neighbourhood of spacelike infinity including past and future null infinity, where the scattering data are posed on an ingoing null cone…

Analysis of PDEs · Mathematics 2025-12-22 Istvan Kadar , Lionor Kehrberger

We construct semiglobal singular spacetimes for the Einstein equations coupled to a massless scalar field. Consistent with the heuristic analysis of Belinskii, Khalatnikov, Lifshitz or BKL for this system, there are no oscillations due to…

Mathematical Physics · Physics 2020-05-08 Andrea Nützi , Michael Reiterer , Eugene Trubowitz

In this paper we study global nonlinear stability for a system of semilinear wave and Klein-Gordon equations with quadratic nonlinearities. We consider nonlinearities of the type of wave-Klein-Gordon interactions where there are no…

Analysis of PDEs · Mathematics 2023-03-14 Qian Zhang

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…

General Relativity and Quantum Cosmology · Physics 2017-10-04 A. Molina , E. Ruiz

The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy…

General Relativity and Quantum Cosmology · Physics 2020-02-19 M. Sharif , Arfa Waseem

We investigate the Einstein vacuum equations as well as the Einstein-null fluid equations describing neutrino radiation. We find new structures in gravitational waves and memory for asymptotically-flat spacetimes of slow decay. These…

General Relativity and Quantum Cosmology · Physics 2021-06-07 Lydia Bieri

We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…

General Relativity and Quantum Cosmology · Physics 2012-01-17 Romain Gicquaud

In this paper we prove the non-linear stability of a system of non-linear wave equations satisfying the weak null condition. In particular, this includes the case of the non-linear stability of Minkowski spacetime times a $d$-torus subject…

General Relativity and Quantum Cosmology · Physics 2019-01-30 Zoe Wyatt

This paper proves global existence and sharp pointwise decay for solutions to nonlinear wave equations satisfying the semilinear null condition, on a class of three-dimensional, asymptotically flat, and notably, non-stationary spacetimes.…

Analysis of PDEs · Mathematics 2026-01-06 Shi-Zhuo Looi , Mihai Tohaneanu
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