ABSTRACT
In the 1970’s, progress on causality theory, singularity theory, and black holes in general relativity, described in the influential text of S. W. Hawking and G. F. R. Ellis, resulted in a resurgence of interest in global Lorentzian geometry. Indeed, a better understanding of global Lorentzian geometry was required for the development of singularity theory. Geodesic completeness, or more accurately geodesic incompleteness, played a crucial role in the development of singularity theory in general relativity and has been thoroughly explored within this framework. Some of the properties of the Lorentzian distance function needed in general relativity had been briefly described in Hawking and Ellis. Hence, as part of the first edition, a systematic study of the Lorentzian distance function was made. The Lorentzian distance function has many similarities with the Riemannian distance function but also many differences.
