Chapter 15: TOV Existence and the Star Builder

The Tolman–Oppenheimer–Volkoff (TOV) equation is the master equation of relativistic stellar structure: it determines the pressure–density profile of a static, spherically symmetric star in hydrostatic equilibrium. In orthodox GR, the TOV equation is an ODE derived from the Einstein equations with a perfect-fluid source, and its solutions define the family of equilibrium stellar models—white dwarfs, neutron stars, and the mass thresholds that separate stable configurations from gravitational collapse.

This chapter derives the τ-native analogue. Instead of an ODE on a manifold, the star builder is a witness construction in the boundary holonomy algebra: given a particle count n and a sector index k, the canonical star builder Star_n(k) constructs the unique equilibrium configuration as a boundary character (§). The construction begins with the spherical carrier predicate (§), which specifies what “spherically symmetric” means in the τ-framework; introduces the GR tension functional (§), which measures the departure from flat-torus equilibrium; derives neutron star structure from the neutron node predicate (§); proves the stability of the neutron node under EW perturbations (§); and derives the Chandrasekhar limit as a relational threshold (§).