Matter Maps to Geometry in Gravitational Collapse

Abstract

We establish an exact bidirectional map between the effective homogeneous interior density of a collapsing star and the exterior metric function in generalized Oppenheimer--Snyder collapse. The Darmois--Israel junction conditions reduce this relation to a purely algebraic form, providing a direct way to reconstruct candidate static geometries and their surface dynamics without solving the corresponding differential field equations separately. Correction powers diagnose models: integer exponents signal ultraviolet completions, while fractional powers identify phenomenological ones. Our framework not only simplifies the construction of regular black holes but also provides a universal benchmark for testing singularity resolution and cosmic censorship in quantum gravity phenomenology.

21 pages, 1 figures

References in corpus (11)

• Formation and evaporation of non-singular black holes
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Gedanken Experiments to Destroy a Black Hole II: Kerr-Newman Black Holes Cannot be Over-Charged or Over-Spun
• Einsteinian cubic gravity
• Quantum Oppenheimer-Snyder and Swiss Cheese models
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Constraining the number of horizons with energy conditions
• Rainbow Black Hole From Quantum Gravitational Collapse
• Covariant dynamics from static spherically symmetric geometries
• Gravitational Collapse: Generalizing Oppenheimer-Snyder and a Conjecture on Horizon Formation Time