Relativity and Cosmology

Chronology Protection and the Formation of Kerr Black Holes from Gravitational Collapse: A Convergent Analysis

Authors: Moninder Singh Modgil, Dnyandeo Dattatray Patil

The maximally extended Kerr spacetime contains closed timelike curves (CTCs) in the regionbeyond its inner Cauchy horizon, in apparent conflict with Hawking’s Chronology ProtectionConjecture (CPC). If gravitational collapse of a rotating star terminates in the Kerrgeometry as the no-hair theorems suggest, the resulting black hole interior would contain aregion of causality violation. We confront this tension by combining four logically independentlines of argument which converge on the same conclusion: the CTC-containing regionis not physically realised in collapse. (i) A classical no-go follows from Cauchy-horizon massinflation: the work of Poisson and Israel, of Ori, and the rigorous instability theorems ofDafermos and of Dafermos—Luk imply that the inner horizon evolves generically into a weaknull curvature singularity, and the maximally extended region containing CTCs is excisedfrom the physical spacetime. (ii) A semiclassical argument computes the leading divergenceof the renormalised stress—energy tensor ⟨Tμν⟩ren for a free scalar field on the Kerr backgroundas the chronology horizon is approached; we recover the universal ⟨Tμν⟩ren ∼ ε−4scaling in the proper distance ε, demonstrating that the semiclassical Einstein equationsbreak down before any CTC can form. (iii) A constructive argument exhibits an explicitone-parameter family of axisymmetric interior metrics which match the Kerr exterior at theevent horizon via the Israel—Darmois junction conditions, keep gϕϕ > 0 throughout the interior,satisfy the dominant and null energy conditions, and admit a global Cauchy surface.(iv) An observational argument turns the empirical record on rapidly rotating pulsars andastrophysical black holes into a quantitative constraint on CPC: anomalies in higher-ordermultipole moments, quasi-normal mode (QNM) frequencies, gravitational-wave echo templates,and the I—Love—Q relations would be required if CPC failed at the level demanded byclassical Kerr formation, and the absence of these anomalies bounds the room available forCTC-permitting endpoints. The four arguments are independent in their assumptions andcomplementary in their domains of validity; their convergence provides a robust case thatCPC holds for rotating gravitational collapse, and that any complete quantum-gravitationalendpoint must preserve global hyperbolicity in the physically accessible region.

Comments: 33 Pages.

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[v1] 2026-05-27 04:26:50

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