Computational Cosmic Censorship

Abstract

We identify a two-gap complexity structure underlying a holographic obstruction to reaching extremality and to the black-hole-mediated route toward weak cosmic censorship violation. The complexity of formation of extremal AdS black holes diverges logarithmically, while it is finite for every subextremal member of the stationary family. We compute the on-shell Wheeler--DeWitt action of overcharged Reissner--Nordstr\"om--AdS in general dimension $D\geq4$. In the minimal prescription, defined by omission of the Maxwell boundary term, the individually divergent Maxwell bulk, on-shell Einstein--Hilbert, and Gibbons--Hawking--York terms cancel exactly. We also evaluate the null--timelike joints and null-boundary counterterms explicitly and show that their combined lower-endpoint contribution vanishes. Adding the Maxwell boundary term produces only a prescription-dependent, regulator-local power-law divergence; no prescription produces a logarithmic divergence, and the corresponding vacuum-subtracted complexity=volume complexity of formation is finite. In the complexity=action and complexity=volume prescriptions, the reverse triangle inequality for complexity distance then implies divergent relative complexity across each adjacent gap. Under a finite-complexity-growth assumption, this gives a conditional obstruction to traversing the stationary path from subextremal black holes through extremality to the superextremal naked-singularity sector.