The Upper Bound of Event Horizon Formation Time in Generalized Oppenheimer-Snyder Collapse

TL;DR

This paper establishes a theoretical upper bound on the time it takes for an event horizon to form during a generalized Oppenheimer-Snyder collapse, showing the Schwarzschild case maximizes this time among similar black holes.

Contribution

It proves that the Schwarzschild exterior maximizes event horizon formation time among all asymptotically flat, static, spherically symmetric black holes with the same mass.

Findings

Schwarzschild maximizes event horizon formation time

Derived a temporal inequality extending Penrose inequality

Bound of T_{eh} = 19/6 m for horizon formation time

Abstract

We prove that, in the framework of the Oppenheimer-Snyder collapse, the Schwarzschild exterior maximizes the event horizon formation time $\Delta T_{\text{eh}}=\frac{19}{6}m$ among all asymptotically flat, static, spherically-symmetric black holes with the same ADM mass $m$ that satisfy the weak energy condition. This bound extends the typical black hole inequalities--such as the Penrose inequality, which constrains spatial geometry--to temporal setting.