Non-Unique Black-Hole Interior Completions
Year: 2026
Type: preprint
Abstract: The exterior geometry of a black hole need not determine a unique interior once the allowed matter and junction class are left open. We formulate this as a one-sided completion problem, distinct from the unique Cauchy evolution of complete initial data. Generic low-regularity changes in transverse horizon geometry produce a Barrab\`es--Israel null shell, and in spherical symmetry Birkhoff's theorem excludes a genuinely new smooth vacuum interior. In an unrestricted smooth effective-source class, however, we give a general shell-free deformation construction: deformations confined to the black-hole side can match a seed metric to all orders at the horizon and preserve the same exterior and event horizon. Inequivalence in this general construction is proved only after adding a labelled interior sequence to the comparison data. Our stronger result is an explicit unaugmented singular/regular pair of shell-free completions for Schwarzschild and every subextremal Kerr exterior. The regular member, constructed from a smooth Kerr--Schild mass profile, has bounded curvature, a source of compact spatial support, the exact vacuum exterior to all orders, and an exactly flat core. The results establish non-uniqueness of one-sided completion data, not of the Einstein Cauchy problem, and do not determine which completion is physically realized.
Author: Rahman, Sabbir
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7127433017