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Related papers: On complete stationary vacuum initial data

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A closed explicit representation of the vacuum Einstein equations in terms of components of curvature 2-forms is given. The discussion is restricted to the case of non-vanishing cubic invariant of conformal curvature spinor. The complete…

General Relativity and Quantum Cosmology · Physics 2009-10-28 Yuri N. Obukhov , Sergey I. Tertychniy

We show that every conformal vector field on a Damek-Ricci space is necessarily Killing, establishing a strong form of infinitesimal conformal rigidity. Although this rigidity phenomenon is classically known in the Einstein setting, our…

Differential Geometry · Mathematics 2026-02-11 Hiroyasu Satoh , Hemangi Madhusudan Shah

The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in $d\geq5$ dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of…

High Energy Physics - Theory · Physics 2015-03-17 Gustavo Dotti , Julio Oliva , Ricardo Troncoso

We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein equations together with the energy-momentum tensor of a barotropic perfect fluid.…

Analysis of PDEs · Mathematics 2020-09-30 Tetu Makino

We consider a characteristic problem of the vacuum Einstein equations with part of the initial data given on a future complete null cone with suitable decay, and show that the solution exists uniformly around the null cone for general such…

General Relativity and Quantum Cosmology · Physics 2014-06-03 Junbin Li , Xi-Ping Zhu

Global properties of maximal future Cauchy developments of stationary, m-dimensional asymptotically flat initial data with an outer trapped boundary are analyzed. We prove that, whenever the matter model is well posed and satisfies the null…

General Relativity and Quantum Cosmology · Physics 2015-06-05 Marc Mars , Martin Reiris

We give a geometric criterion for the breakdown of an Einstein vacuum space-time foliated by a constant mean curvature, or maximal, foliation. More precisely we show that the foliated space-time can be extended as long as the the second…

Analysis of PDEs · Mathematics 2008-01-28 S. Klainerman , I. Rodnianski

The approach, referred to as "monodromy transform", provides some general base for solution of all known integrable space - time symmetry reductions of Einstein equations for the case of pure vacuum gravitational fields, in the presence of…

General Relativity and Quantum Cosmology · Physics 2007-05-23 G. A. Alekseev

We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Milton Ruiz , Oliver Rinne , Olivier Sarbach

We consider a broad class of asymptotically flat, maximal initial data sets satisfying the vacuum constraint equations, admitting two commuting rotational symmetries. We construct a mass functional for `$t-\phi^i$' symmetric data which…

General Relativity and Quantum Cosmology · Physics 2015-06-04 Aghil Alaee , Hari K. Kunduri

This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…

General Relativity and Quantum Cosmology · Physics 2015-09-02 João L. Costa , Pedro M. Girão , José Natário , Jorge Drumond Silva

In this paper, we prove several rigidity results for compact initial data sets, in both the boundary and no boundary cases. In particular, under natural energy, boundary, and topological conditions, we obtain a global version of the main…

General Relativity and Quantum Cosmology · Physics 2023-02-03 Gregory J. Galloway , Abraão Mendes

We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applications include an improvement of the decay rate in…

Analysis of PDEs · Mathematics 2023-07-19 Yuchen Mao , Zhongkai Tao

The geometry of two infinitely long lines of mass moving in a fixed circular orbit is considered as a toy model for the inspiral of a binary system of compact objects due to gravitational radiation. The two Killing fields in the toy model…

General Relativity and Quantum Cosmology · Physics 2016-08-25 John T. Whelan , Joseph D. Romano

This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…

General Relativity and Quantum Cosmology · Physics 2016-08-25 J. Frauendiener

We study a model for gravity in 3+1 dimensions, inspired in general relativity in 2+1 dimensions. In contrast regular general relativity in 3+1 dimensions, the model postulates that space in absence of matter is flat. The requirement that…

General Relativity and Quantum Cosmology · Physics 2011-11-29 Maarten van de Meent

By using the effective field theory approach, we investigate the role of initial condition for the dark energy or modified gravity models. In details, we consider the constant and linear parametrization of the effective Newton constant…

Cosmology and Nongalactic Astrophysics · Physics 2018-01-10 Xue-Wen Liu , Bin Hu , Yi Zhang

We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant.

General Relativity and Quantum Cosmology · Physics 2008-11-26 P. T. Chrusciel , E. Delay

We consider the three-dimensional relativistic Vlasov-Maxwell-Boltzmann system, where the speed of light $c$ is an arbitrary constant no less than 1, and we establish global existence and nonlinear stability of the vacuum for small initial…

Analysis of PDEs · Mathematics 2026-02-06 Chuqi Cao , Xingyu Li

We develop a general method of proving the ellipticity of boundary value problems for the stationary vacuum space time, by showing that the stationary vacuum field equations are elliptic subjected to a geometrically natural collection of…

Differential Geometry · Mathematics 2019-07-12 Zhongshan An