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We devise a new approach for the analysis of issues of geometric pathologiesand black holes of a spacetime, based on a new mass function defined on anideal un-physical spacetime which models time-flow or time dilation. The massfunction is interpreted as an "extra" local energy density that encodes therate at which time comes to a "stop" (hardly visible) or it measures howquickly the (illusory) Event horizon forms. This latter is defined on themanifold with corners resulting from an appropriate conformal compactificationof the original physical space-time, the concrete choice of compactificationbeing tied to the geometric structure of collapsing spacetimes. We define the(illusory) Event horizon as the set of zero-mass function and provideconditions for which it stands as a "black hole's event horizon". As a firstmain result owing to the new definitions here, we establish the existence of alower bound for the "total mass", provided some conditions on the extrinsiccurvature of the space-time are satisfied. The proof builds on geometric flowtechniques. Namely, by flowing the "black hole's event horizon", one is able toderive via a Lagrangian formulation, a Minimization Problem for the "totalmass" and which is addressed under Iso-perimetric constraints' perspective.Prior to this main result, we first provide hypotheses which assure the trappedsurface's formation in this context.

Conformal Scale Geometry of Spacetime -- A lower bound for a total mass