Initial data in general relativity

Gravitational initial data on a spatial manifold consist of a Riemannian metric $h$ and an extrinsic curvature $K$ satisfying the Hamiltonian constraint and momentum constraint. Matter theories require their own data and constraints as well. The data determine a maximal Cauchy development.

A maximal Cauchy development is the largest globally hyperbolic solution, unique up to an appropriate isometry, determined by admissible initial data, with the initial hypersurface a Cauchy hypersurface. It can sometimes be extended as a spacetime across a Cauchy horizon even though that extension is no longer globally determined by the initial hypersurface.

The strong cosmic censorship conjecture asserts that the maximal Cauchy development of generic admissible initial data is inextendible in a specified regularity class. The matter model, topology on initial data, and extension regularity are part of the assertion. An exceptional exact solution with a smooth Cauchy horizon need not violate this generic claim.