Matter Maps to Geometry in Gravitational Collapse

TL;DR

This paper introduces an exact algebraic mapping between the interior matter density and exterior geometry in gravitational collapse, simplifying Einstein's equations and enabling analysis of singularity resolution.

Contribution

It provides a novel algebraic framework linking matter and geometry in collapse models, facilitating classical and quantum corrections without solving differential equations.

Findings

Algebraic map reduces Einstein's equations to simpler forms.

Correction powers indicate ultraviolet or phenomenological models.

Framework enables systematic testing of singularity resolution.

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.