Related papers: Gluing and wormholes for the Einstein constraint e…
In this paper, we sketch the proof of the extension of the stability theorem of the Minkowski space in General Relativity done explicitly in previous work by the present author. We discuss solutions of the Einstein vacuum (EV) equations. We…
We have found a simple exact solution of spherically-symmetrical Einstein equations describing a wormhole for an inhomogeneous distribution of the phantom energy. The equation of state is linear but highly anisotropic: while the radial…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are…
Static and spherically symmetric wormhole solutions can be reconstructed in the framework of curvature based Extended Theories of Gravity. In particular, extensions of the General Relativity, in metric and curvature formalism give rise to…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains…
The techniques developed by Butscher in arXiv:math/0703469 for constructing constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere by gluing together spherical building blocks are generalized to handle less symmetric initial…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
We study solutions to the static vacuum Einstein equations on exterior domains with prescribed metric and mean curvature on the inner boundary. It is proved that for any such boundary data near the standard round boundary data in Euclidean…
We present the first analysis of traversable wormhole solutions within the framework of Einstein-aether theory. We show that the corresponding field equations admit three distinct wormhole geometries, obtained by adopting three different…
In this work we show that Einstein gravity in four dimensions can be consistently obtained from the compactification of a generic higher curvature Lovelock theory in dimension $D=4+p$, being $p\geq1$. The compactification is performed on a…
Local solutions are a vivid and long-living topic in gravitational physics. We consider exact static pseudo-spherically symmetric solutions of semi-classical Einstein's equations in presence of the trace anomaly contribution. We investigate…
Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological…
In this paper, we initiate the study of characteristic event horizon gluing in vacuum. More precisely, we prove that Minkowski space can be glued along a null hypersurface to any round symmetry sphere in a Schwarzschild black hole spacetime…
The condition R=0, where R is the four-dimensional scalar curvature, is used for obtaining a large class (with an arbitrary function of r) of static, spherically symmetric Lorentzian wormhole metrics. The wormholes are globally regular and…
We describe a numerical method to construct Cauchy data extending to space-like infinity based on Corvino's (2000) gluing method. Adopting the setting of Giulini and Holzegel (2005), we restrict ourselves here to vacuum axisymmetric…
Wormholes can be described as geometrical structures in space and time that can serve as connection between distant regions of the universe. Mathematically, general wormholes can be defined both on stationary as well as on dynamic line…