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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

Ricci-flat solutions to Einstein's equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy--momentum tensor is expanded in…

High Energy Physics - Theory · Physics 2023-12-19 Andrea Campoleoni , Arnaud Delfante , Simon Pekar , P. Marios Petropoulos , David Rivera-Betancour , Matthieu Vilatte

We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for…

General Relativity and Quantum Cosmology · Physics 2012-11-29 William E. East , Fethi M. Ramazanoğlu , Frans Pretorius

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

Numerical Analysis · Mathematics 2021-12-24 Jennifer Scott , Miroslav Tuma

We consider the 4+1 Einstein's field equations (EFE's) in vacuum, simplified by the assumption that there is a four-dimensional sub-manifold on which an isometry group of dimension four acts simply transitive. In particular we consider the…

General Relativity and Quantum Cosmology · Physics 2018-07-11 T. Pailas , Petros A. Terzis , T. Christodoulakis

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

Perturbations of the linearized vacuum Einstein equations on a null cone in the Bondi-Sachs formulation of General Relativity can be derived from a single master function with spin weight two, which is related to the Weyl scalar \Psi_0, and…

General Relativity and Quantum Cosmology · Physics 2015-06-12 Thomas Mädler

We construct a family of asymptotically flat Cauchy initial data for the Einstein vacuum equations that contain no trapped surfaces, yet whose future development admits multiple causally independent trapped surfaces. Assuming the weak…

General Relativity and Quantum Cosmology · Physics 2025-06-23 Dawei Shen , Jingbo Wan

We study the initial value problem in Einstein-Cartan theory which includes torsion and, therefore, a non-symmetric connection on the spacetime manifold. Generalizing the path of a classical theorem by Choquet-Bruhat and York for the…

General Relativity and Quantum Cosmology · Physics 2025-05-29 Paulo Luz , Filipe C. Mena

We give a formulation of the vacuum Einstein equations in terms of a set of volume-preserving vector fields on a four-manifold ${\cal M}$. These vectors satisfy a set of equations which are a generalisation of the Yang-Mills equations for a…

General Relativity and Quantum Cosmology · Physics 2010-04-06 James D. E. Grant

We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…

General Relativity and Quantum Cosmology · Physics 2009-03-19 K. Komathiraj , S. D. Maharaj

Generalising an analysis of Corvino and Schoen, we study surjectivity properties of the constraint map in general relativity in a large class of weighted Sobolev spaces. As a corollary we prove several perturbation, gluing, and extension…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Piotr T. Chrusciel , Erwann Delay

We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…

General Relativity and Quantum Cosmology · Physics 2009-10-16 S. D. Maharaj , S. Thirukkanesh

In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein--Euler equations of general relativity based on a first order…

General Relativity and Quantum Cosmology · Physics 2024-02-22 Michael Dumbser , Olindo Zanotti , Elena Gaburro , Ilya Peshkov

We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…

General Relativity and Quantum Cosmology · Physics 2012-08-21 Ricardo E. Gamboa Saravi

We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized…

Differential Geometry · Mathematics 2023-01-20 John Anderson , Justin Corvino , Federico Pasqualotto

We set up an Einstein-Gauss-Bonnet theory in four dimensions, based on the recent formulation of pure gravity with extra dimensions of vanishing metrical length [1]. In absence of torsion, the effective field equations depend only on the…

General Relativity and Quantum Cosmology · Physics 2022-02-11 Sandipan Sengupta

We solve the Einstein constraint equations for a 3 + 1 dimensional vacuum spacetime with a space-like translational Killing field in the asymptotically flat case.. The presence of a space-like translational Killing field allows for a…

Analysis of PDEs · Mathematics 2014-10-23 Cécile Huneau

Modified gravity theories such as Einstein scalar Gauss Bonnet (EsGB) contain higher derivative terms in the spacetime curvature in their action, which results in modifications to the Hamiltonian and momentum constraints of the theory. In…

General Relativity and Quantum Cosmology · Physics 2023-12-01 Sam E. Brady , Llibert Aresté Saló , Katy Clough , Pau Figueras , Annamalai P. S

We construct explicit rotating solutions in Einstein's theory of relativity with a minimally coupled free scalar field rederiving and finding solutions in four or five spacetime dimensions. These spacetimes describe, in particular, the…

General Relativity and Quantum Cosmology · Physics 2025-06-18 José Barrientos , Christos Charmousis , Adolfo Cisterna , Mokhtar Hassaine