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, Einsteins 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.
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