Abstract null hypersurfaces and characteristic initial value problems in General Relativity

TL;DR

This thesis explores the geometry and initial value problems of null hypersurfaces in General Relativity, focusing on hypersurface data, characteristic problems, Killing data, and conformal infinity.

Contribution

It develops a unified formalism for hypersurface data and analyzes characteristic initial value problems and null infinity in a comprehensive manner.

Findings

Formalism of hypersurface data is unified and extended.

Analysis of characteristic Cauchy problem in a detached framework.

Investigation of the geometry of conformal null infinity.

Abstract

This thesis is framed within the field of Mathematical Relativity and is organized into six chapters. After an introduction to the topic in Chapter 1, Chapter 2 reviews and further develops the formalism of hypersurface data, which provides the unifying framework for the entire thesis. In Chapter 3 we study the characteristic Cauchy problem from a fully detached perspective. Chapter 4 is devoted to the Killing initial data problem, also analyzed within this detached framework. In Chapter 5 we investigate the transverse (or asymptotic) expansion of the metric at a general null hypersurface. Finally, Chapter 6 addresses the geometry of conformal null infinity.