  Every spacetime is defined by its metric, the mathematical object which
further defines the spacetime curvature. From the relativity principle, we have
the freedom to choose which coordinate system to write our metric in. Some
coordinate systems, however, are better than others. In this text, we begin
with a brief introduction into general relativity, Einstein's masterpiece
theory of gravity. We then discuss some physically interesting spacetimes and
the coordinate systems that the metrics of these spacetimes can be expressed
in. More specifically, we discuss the existence of the rather useful unit-lapse
forms of these spacetimes. Using the metric written in this form then allows us
to conduct further analysis of these spacetimes, which we discuss.
