相关论文: Numerical Bifurcation Analysis of the Conformal Me…

As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…

We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the…

Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…

This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at AEI in the last years, and discuss a…

We prove that in a certain class of conformal data on an asymptotically cylindrical manifold, if the conformally decomposed Einstein constraint equations do not admit a solution, then one can always find a nontrivial solution to the limit…

Numerical evolutions of a system of equations close to null infinity in the geometric background of the inversion-Minkowski spacetime are performed. The evolved equations correspond to the linearisation of a second order metric formulation…

This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the…

Uniqueness problems in the elliptic sector of constrained formulations of Einstein equations have a dramatic effect on the physical validity of some numerical solutions, for instance when calculating the spacetime of very compact stars or…

Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a…

We study the appearance of multiple solutions to certain decompositions of Einstein's constraint equations. Pfeiffer and York recently reported the existence of two branches of solutions for identical background data in the extended…

In this note we prove two existence theorems for the Einstein constraint equations on asymptotically Euclidean manifolds. The first is for arbitrary mean curvature functions with restrictions on the size of the transverse-traceless data and…

In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by…

In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…

Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated…

A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace…

We apply verified numerics to the Nirenberg problem, proving that a genuine solution exists near two given computer-generated approximate solutions. This proves existence of a solution for a particular prescribed curvature that was…

CIPM published the Supplement I for GUM in 2008 as not only an alternative approach to estimate the uncertainty for a given calibration measurement but also as a proper uncertainty estimation one, whenever any of the conditions imposed in…

We prove the existence of a large class of initial data for the vacuum Einstein equations which possess a finite number of asymptotically Euclidean and asymptotically conformally cylindrical or periodic ends. Aside from being asymptotically…

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…

The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This…