Matter Maps to Geometry in Gravitational Collapse

Abstract

We establish an exact bidirectional map between interior Friedmann density of a collapsing star and exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse. This reduces Einstein's differential matter-geometry relation to an algebraic form, generating classical or quantum-corrected metrics and dynamics without solving field equations. Correction powers diagnose models: integer exponents signal ultraviolet completions, while fractional powers identify phenomenological ones. Our framework enables systematic tests of singularity resolution and cosmic censorship.