Fuchsian methods and spacetime singularities

TL;DR

This paper surveys Fuchsian methods and their applications in understanding spacetime singularities, discussing existence questions for spacetimes with compact Cauchy horizons and potential future research directions.

Contribution

It provides a comprehensive overview of Fuchsian techniques in general relativity and explores their role in analyzing spacetime singularities and Cauchy horizons.

Findings

Fuchsian equations are effective in studying spacetime singularities.

Various applications of Fuchsian methods in general relativity are outlined.

Future research directions for Fuchsian methods are suggested.

Abstract

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated.