Horizon formation from effective matter profiles in static spacetimes

Abstract

The formation of event horizons is traditionally studied as the endpoint of gravitational collapse, where the matter distribution and the spacetime geometry are evolved simultaneously toward a black hole state. In this work, we consider the inverse problem: given a static geometry containing the simplest causally exposed singular structure, namely a timelike naked singularity, what are the minimal conditions on the surrounding matter required for the emergence of an event horizon? Within classical general relativity, we derive sufficient conditions for horizon formation in terms of the radial organization, compactness and finiteness of the matter distribution. These conditions are summarized by a simple geometric criterion that determines whether a static configuration becomes causally inaccessible to external observers. We further identify situations in which horizon formation necessarily fails, thereby characterizing both the existence and obstruction of causal cloaking in static spacetimes. Our results show that the emergence of an event horizon is not controlled solely by the total amount of matter, but rather by the way mass-energy is radially accumulated. This provides a minimal and geometrically transparent framework for understanding horizon formation as a causal transition in static spacetimes, independent of gravitational collapse or dynamical evolution.

8 pages, 1 figure