We study dynamical surface gravity in a general spherically symmetric settingusing Painlev\'{e}-Gullstrand (PG) coordinates. Our analysis includes severaldefinitions that have been proposed in the past as well as two new definitionsadapted to PG coordinates. Various properties are considered, including generalcovariance, value at extremality, locality and static limit. We illustrate withspecific examples of "dirty" black holes that even for spacetimes possessing aglobal timelike Killing vector, local definitions of surface gravity can differsubstantially from "non-local" ones that require an asymptotic normalizationcondition. Finally, we present numerical calculations of dynamical surfacegravity for black hole formation via spherically symmetric scalar fieldcollapse. Our results highlight the differences between the various definitionsin a dynamical setting and provide further insight into the distinction betweenlocal and non-local definitions of surface gravity.
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