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Related papers: Stationary solutions and asymptotic flatness II

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In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic 3-space H^3. Galvez, Martinez and Milan showed that when the singular set does not accumulate at an end, the end is asymptotic to a…

Differential Geometry · Mathematics 2009-08-03 Masatoshi Kokubu , Wayne Rossman , Masaaki Umehara , Kotaro Yamada

We study series of the stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent with the exterior solutions in some class of the scalar-tensor theories of…

General Relativity and Quantum Cosmology · Physics 2010-11-19 Tooru Tsuchida , Kazuya Watanabe

We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the…

Mathematical Physics · Physics 2015-05-19 Filipe C. Mena

In a recent research on degenerate points of steady axisymmetric gravity flows with general vorticity, it has been shown that the possible asymptotics near any stagnation point must be the "Stokes corner", the "horizontal cusp", or the…

Analysis of PDEs · Mathematics 2023-12-07 Lili Du , Chunlei Yang

This is the second in a two part series of papers concerning Morse quasiflats - higher dimensional analogs of Morse quasigeodesics. Our focus here is on their asymptotic structure. In metric spaces with convex geodesic bicombings, we prove…

Metric Geometry · Mathematics 2023-04-28 Jingyin Huang , Bruce Kleiner , Stephan Stadler

In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of…

Analysis of PDEs · Mathematics 2010-06-07 Daniel Tataru

For any non-rotating effective quantum (uncharged) black hole model to be viable, its asymptotic structure of spacetime should reduce to that of a Schwarzschild black hole. After examining the asymptotic structure of quantum black holes…

General Relativity and Quantum Cosmology · Physics 2020-08-05 Mariam Bouhmadi-López , Suddhasattwa Brahma , Che-Yu Chen , Pisin Chen , Dong-han Yeom

We consider the Hartree and Schr\"{o}dinger equations describing the time evolution of wave functions of infinitely many interacting fermions in three-dimensional space. These equations can be formulated using density operators, and they…

Analysis of PDEs · Mathematics 2026-01-14 Sonae Hadama

The problem of existence of spacelike hypersurfaces with constant mean curvature in asymptotically flat spacetimes is considered for a class of asymptotically Schwarzschild spacetimes satisfying an interior condition. Using a barrier…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Lars Andersson , Mirta S. Iriondo

The unexpected discovery of hairy black hole solutions in theories with scalar fields simply by considering asymptotically Anti de-Sitter, rather than asymptotically flat, boundary conditions is analyzed in a way that exhibits in a clear…

General Relativity and Quantum Cosmology · Physics 2014-11-17 Daniel Sudarsky , Jose Antonio Gonzalez

We show that stationary, asymptotically flat solutions of the electro-vacuum Einstein equations are analytic at $i^0$, for a large family of gauges, in odd space-time dimensions higher than seven. The same is true in space-time dimension…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Robert Beig , Piotr T. Chruściel

This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near…

Probability · Mathematics 2008-09-19 Salah-Eldin A. Mohammed , Tusheng Zhang , Huaizhong Zhao

Following the strategy developed by Chodosh, Li, Minter and Stryker, and using the volume estimate of Antonelli and Xu, we prove that, in $\mathbb R^6$, a complete, two-sided, stable minimal hypersurfaces is flat.

Differential Geometry · Mathematics 2024-05-24 Laurent Mazet

It is proved that a stationary solutions to the vacuum Einstein field equations with non-vanishing angular momentum have no Cauchy slice that is maximal, conformally flat, and non-boosted. The proof is based on results coming from a certain…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Juan A. Valiente Kroon

In this paper we consider a non-linear Schroedinger equation with a cubic nonlinearity and a multi-dimensional double well potential. In the semiclassical limit the problem of the existence of stationary solutions simply reduces to the…

Mathematical Physics · Physics 2015-06-18 Andrea Sacchetti

The current work considers solutions to the wave equation on asymptotically flat, stationary, Lorentzian spacetimes in (1+3) dimensions. We investigate the relationship between the rate at which the geometry tends to flat and the pointwise…

Analysis of PDEs · Mathematics 2020-06-23 Katrina Morgan

We study the asymptotic behavior of flat flow solutions to the periodic and planar two-phase Mullins-Sekerka flow and area-preserving curvature flow. We show that flat flows converge to either a finite union of equally sized disjoint disks…

Differential Geometry · Mathematics 2025-03-11 Vedansh Arya , Daniele De Gennaro , Anna Kubin

This is the second article of a series or two, proving a generalisation of the uniqueness theorem of the Schwarzschild solution. The theorem to be shown classifies all (metrically complete) solutions of the static vacuum Einstein equations…

General Relativity and Quantum Cosmology · Physics 2018-06-05 Martín Reiris Ithurralde

We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…

Analysis of PDEs · Mathematics 2008-05-27 E. Kirr , A. Zarnescu

We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…

Analysis of PDEs · Mathematics 2010-09-03 Robert L. Pego , Shu-Ming Sun