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Under a weak assumption of the existence of a geodesic null congruence, we present the general solution of the Einstein field equations in three dimensions with any value of the cosmological constant, admitting an aligned null matter field,…

General Relativity and Quantum Cosmology · Physics 2021-08-09 Jiri Podolsky , Robert Svarc , Hideki Maeda

We explicitly construct all stationary, non-static, extremal near horizon geometries in $D$ dimensions that satisfy the vacuum Einstein equations, and that have $D-3$ commuting rotational symmetries. Our work generalizes [arXiv:0806.2051]…

General Relativity and Quantum Cosmology · Physics 2010-05-07 Stefan Hollands , Akihiro Ishibashi

In this paper, we systematically study gravitational waves (GWs) produced by remote compact astrophysical sources. To describe such GWs properly, we introduce three scales, $\lambda, \; L_c$ and $L$, denoting, respectively, the typical…

Cosmology and Nongalactic Astrophysics · Physics 2021-06-30 Jared Fier , Xiongjun Fang , Bowen Li , Shinji Mukohyama , Anzhong Wang , Tao Zhu

This article is the second of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. In the present article, we record geometric conclusions obtained by combining the geometric framework…

General Relativity and Quantum Cosmology · Physics 2026-03-03 Hans Ringström

We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly…

Analysis of PDEs · Mathematics 2007-05-23 Giuseppe Ali , John K. Hunter

We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the…

High Energy Physics - Theory · Physics 2015-04-30 Maximilian Demmel , Frank Saueressig , Omar Zanusso

We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the neighborhood of space-like infinity. The result…

Analysis of PDEs · Mathematics 2011-04-21 Hans Lindblad , Igor Rodnianski

Impulsive gravitational waves are (weak) solutions to the Einstein vacuum equations such that the Riemann curvature tensor admits a delta singularity along a null hypersurface. The interaction of impulsive gravitational waves is then…

General Relativity and Quantum Cosmology · Physics 2021-06-11 Jonathan Luk , Maxime Van de Moortel

We obtain a new family of exact vacuum solutions to quadratic gravity that describe pp-waves with two-dimensional wave surfaces that can have any prescribed constant curvature. When the wave surfaces are flat we recover the Peres waves…

General Relativity and Quantum Cosmology · Physics 2024-12-19 Sjors Heefer , Lorens F. Niehof , Andrea Fuster

The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\alpha\beta}$ of a spacetime with vanishing Ricci curvature $R_{\alpha,\beta}$ and prescribed initial data. Under the harmonic gauge condition, the…

Analysis of PDEs · Mathematics 2009-07-23 Lavi Karp

We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the…

Analysis of PDEs · Mathematics 2023-02-28 Peter Hintz

Here we prove the linear stability of a family of `$n+1$'-dimensional Friedmann Lema\^{i}tre Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutions to the linearized Einstein-Euler field equations…

General Relativity and Quantum Cosmology · Physics 2021-10-01 Puskar Mondal

An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…

General Relativity and Quantum Cosmology · Physics 2015-10-07 M. M. Akbar , M. A. H. MacCallum

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 systematically investigate the complete class of vacuum solutions in the Einstein-Gauss-Bonnet gravity theory which belong to the Kundt family of non-expanding, shear-free and twist-free geometries (without gyratonic matter terms) in any…

General Relativity and Quantum Cosmology · Physics 2020-10-14 Robert Svarc , Jiri Podolsky , Ondrej Hruska

We use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and…

General Relativity and Quantum Cosmology · Physics 2020-10-28 Mikael Normann , Juan Valiente Kroon

We show that, given an arbitrary shift, the lapse $N$ can be chosen so that the extrinsic curvature $K$ of the space slices with metric $\overline g$ in arbitrary coordinates of a solution of Einstein's equations satisfies a quasi-linear…

General Relativity and Quantum Cosmology · Physics 2012-08-27 Y. Choquet-Bruhat , J. W. York,

Upcoming gravitational wave-experiments promise a window for discovering new physics in astronomy. Detection sensitivity of the broadband laser interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with accurate…

General Relativity and Quantum Cosmology · Physics 2016-11-03 Maurice H. P. M. van Putten

Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions…

General Relativity and Quantum Cosmology · Physics 2023-04-25 Piotr T. Chruściel

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