Related papers: Cauchy-characteristic matching
General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this…
We describe numerical techniques used in the construction of our 4th order evolution for the full Einstein equations, and assess the accuracy of representative solutions. The code is based on a null gauge with a quasi-spherical radial…
We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in…
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…
The two defining features of the Einsteinian gravity are that it is self interactive as well as it links universally to all particles including zero mass particles. In the process of obtaining the Schwarzshild solution for gravitational…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…
In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…
In this paper we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearisation of the general conformal field equations near spacelike infinity, which is only well-defined in Friedrich's…
A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
This article provides a discussion on the construction of conformal Gaussian gauge systems to study the evolution of solutions to the Einstein field equations with positive Cosmological constant. This is done by means of a gauge based on…
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the…
The details are presented of a new evolution algorithm for the characteristic initial-boundary value problem based upon an affine parameter rather than the areal radial coordinate used in the Bondi-Sachs formulation. The advantages over the…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
We consider general relativistic Cauchy data representing two nonspinning, equal-mass black holes boosted toward each other. When the black holes are close enough to each other and their momentum is sufficiently high, an encompassing…
Self-accelerating solutions in massive gravity provide explicit, calculable examples that exhibit the general interplay between superluminality, the well-posedness of the Cauchy problem, and strong coupling. For three particular classes of…
Wormhole solutions in gravitational theories typically require exotic matter. Here we present a wormhole solution to the field equations of Einsteinian Cubic Gravity -- a phenomenological competitor to general relativity that includes terms…
We consider gravitational field equations which are Einstein equations written in terms of embedding coordinates in some higher dimensional Minkowski space. Our main focus is to address some tricky issues relating to the Cauchy problem and…
The classical and quantum properties of a new solution obtained in $2+1$% -dimensional gravity coupled with a real scalar field is analyzed in detail. The considered new solution is a one-parameter generalization of a previously known…