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Caterina Vâlcu

Publications and source records attributed to Caterina Vâlcu.

3 recordsLinked to original sources
arXiv2021

Einstein Constraint Equations for Kaluza-Klein Spacetimes

The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the conformal method to reduce the constraint equations to a system of elliptic equation and work in the near CMC (constant mean curvature) regime. The main new feature of our paper is the introduction of new weighted Sobolev spaces, adapted to the inversion of the Laplacian on product manifolds.

math.AP↗
arXiv2020

Stability for small data: the drift model of the conformal method

The conformal method in general relativity aims to successfully parametrise the set of all initial data associated with globally hyperbolic spacetimes. One such mapping was suggested by David Maxwell. I verify that the solutions of the corresponding conformal system are stable, in the sense that they present a priori bounds under perturbations of the system's coefficients. This result holds in dimensions $3\leq n\leq 5$, when the metric is conformally flat, the drift is small. A scalar field with suitably high potential is considered in this case.

math.AP↗