We investigate the conditions under which black hole fragmentation, the splitting of a black hole into two or multiple smaller ones, may occur via an unspecified dynamics, which would have the topology of a pair-of-pants. We employ kinematical and entropical consideration on time-sliced quasistatic black hole configurations to check under what conditions the pants dynamics is permitted. In classical general relativity, the Bekenstein-Hawking area law forbids such processes for Schwarzschild black holes. For spinning Kerr black holes, purely kinematic analyses impose constraints that prevent fragmentation, even in regimes where entropy considerations might allow it, except possibly in near-extremal cases. We then hunt for scenarios where black holes can wear pants: from the well-known Gregory-Laflamme instability in higher dimensions, to the potential effect of superradiant instabilities in nonaxisymmetric radiation trapping, to finally gravitational models that modify the relations between entropy and/or horizon radius and the black hole mass in four dimensions. In all such cases, emission of small fragments can be entropically favored. However, its occurrence still depends on the kinematic configuration of the initial state. Our analysis clarifies the theoretical landscape where black holes may fragment, which is particularly relevant for primordial black holes and catastrophic events such as black hole mergers.

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• Classical black holes
• Quantum aspects of black holes