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We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the…

General Relativity and Quantum Cosmology · Physics 2017-12-11 Ellery Ames , Florian Beyer , James Isenberg , Philippe G. LeFloch

In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite…

Analysis of PDEs · Mathematics 2019-06-07 John Anderson , Federico Pasqualotto

We consider the problem of small data global existence for quasilinear wave equations with null condition on a class of Lorentzian manifolds $(\mathbb{R}^{3+1}, g)$ with \textbf{time dependent} inhomogeneous metric. We show that…

Analysis of PDEs · Mathematics 2015-06-18 Shiwu Yang

This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us…

Analysis of PDEs · Mathematics 2017-01-02 Philippe G. LeFloch

We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the…

Mathematical Physics · Physics 2026-04-02 Stefano Galanda , Paolo Meda , Simone Murro , Nicola Pinamonti , Gabriel Schmid

We consider the existence and stability of the Einstein static universe under the Generalized Uncertainty Principle (GUP) effects. We show that this solution in the presence of perfect fluid with a minimal length is cyclically stable around…

General Relativity and Quantum Cosmology · Physics 2017-05-25 K. Atazadeh , F. Darabi

We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…

Analysis of PDEs · Mathematics 2015-02-17 Bruno Premoselli

We study the static cosmological solutions and their stability at background level in the framework of massive bigravity theory with Friedmann-Robertson-Walker (FRW) metrics. By the modification proposed in the cosmological equations…

General Relativity and Quantum Cosmology · Physics 2017-05-17 M. Mousavi , F. Darabi

We consider the coupled systems of nonlinear wave and Klein-Gordon equations in two space dimensions with cubic nonlinearity. For this kind of systems, the small data global existence is already known if the cubic nonlinearity satisfies a…

Analysis of PDEs · Mathematics 2022-05-30 Minggang Cheng

A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Paul R. Anderson , Carmen Molina-Paris , Emil Mottola

We study the nonlinear stability of the $(3+1)$-dimensional Minkowski spacetime as a solution of the Einstein vacuum equation. Similarly to our previous work on the stability of cosmological black holes, we construct the solution of the…

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

We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy…

General Relativity and Quantum Cosmology · Physics 2018-07-10 F. Darabi , K. Atazadeh , Y. Heydarzade

Consider the characteristic initial value problem for the Einstein vacuum equations without any symmetry assumptions. Impose a sequence of data on two intersecting null hypersurfaces, each of which is foliated by spacelike $2$-spheres.…

Analysis of PDEs · Mathematics 2020-09-21 Jonathan Luk , Igor Rodnianski

A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…

Differential Geometry · Mathematics 2020-01-08 Oliver Lindblad Petersen

It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…

General Relativity and Quantum Cosmology · Physics 2016-05-13 Jonathan Luk , Sung-Jin Oh , Shiwu Yang

The stability of an Einstein static universe in the DGP braneworld scenario is studied in this paper. Two separate branches denoted by $\epsilon=\pm1$ of the DGP model are analyzed. Assuming the existence of a perfect fluid with a constant…

General Relativity and Quantum Cosmology · Physics 2014-11-21 Kaituo Zhang , Puxun Wu , Hongwei Yu

In the present work we consider the existence and stability of Einstein static {\sf ES} Universe in Brans-Dicke ({\sf BD}) theory with non-vanishing spacetime torsion. In this theory, torsion field can be generated by the {\sf BD} scalar…

General Physics · Physics 2019-03-26 Hamid Shabani , Amir Hadi Ziaie

We prove a global well-posedness and asymptotic convergence theorem for the \((3+1)\)-dimensional vacuum Einstein equations with positive cosmological constant \(\Lambda\) on globally hyperbolic spacetimes \(\widetilde M \cong M \times…

General Relativity and Quantum Cosmology · Physics 2026-04-07 Puskar Mondal

We study the stability properties of the Kidder-Scheel-Teukolsky (KST) many-parameter formulation of Einstein's equations for weak gravitational waves on flat space-time from a continuum and numerical point of view. At the continuum,…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Gioel Calabrese , Jorge Pullin , Olivier Sarbach , Manuel Tiglio

In the middle of last century, Bondi and his coworkers proposed an out going boundary condition for the Einstein equations. Based on such boundary condition the authors theoretically solved the puzzle of the existence problem of…

General Relativity and Quantum Cosmology · Physics 2017-10-17 Xiaokai He , Zhoujian Cao , Jiliang Jing