Living Reviews in Relativity: "The general relativistic constraint equations"

Carlotto, A. The general relativistic constraint equations. Living Rev Relativ 24, 2 (2021). https://doi.org/10.1007/s41114-020-00030-z

Open Access | Review Article

Published: 24 February 2021

"This article will for quite some time be a main reference for mathematicians doing abstract basic work on the equations as well as for relativists interested in physical application sof these results."  [from referee report]

Abstract:

We present the state-of-the-art concerning the relativistic constraints, which describe the geometry of hypersurfaces in a spacetime subject to the Einstein field equations. We review a variety of solvability results, the construction of several classes of solutions of special relevance and place results in the broader context of mathematical general relativity. Apart from providing an overview of the subject, this paper includes a selection of open questions, as well as a few complements to some significant contributions in the literature.

The author: 

Alessandro Carlotto is a professor in the Department of Mathematics at the ETH Zurich.  His research lies at the interface of Differential Geometry, Nonlinear Analysis and Mathematical Physics, with special focus on geometric variational problems arising in contexts ranging from general relativity to conformal geometry.