Pauli Principle Modification and Its Astrophysical Consequences in Noncommutative Spectral Geometry

We investigate the modifications to the Pauli exclusion principle arising from the geometric structure of fermions as tori T 2 in noncommutative spectral geometry, and explore their profound astrophysical consequences. In this framework, fermions are not point particles but extended topological objects with characteristic scaleRc ∼ Λ−1NC, and their anticommutation relations receive corrections controlled by the noncommutativity parameter θ:{ψ(x),ψ†(y)} = δθ(x − y), (1)where δθ has a width ∼ p|θ|.We derive the modified equation of state for degenerate fermion gases and apply it to three key astrophysical systems:1. White dwarfs: The modification to the Chandrasekhar limit is negligible (∆M/M ∼ 10−76), preserving the role of Type Ia supernovae as standard candles. However, the existence of super-Chandrasekhar white dwarfs is possible through other mechanisms in the model.2. Neutron stars: The direct pressure correction is tiny (∼ 10−68), but nonperturbative topological effects suppress exotic phases (hyperons, quark matter), allowing maximum masses up to 2.5−3.0M⊙. This naturally explains the existence of massive pulsars like PSR J0952-0607 (∼ 2.35M⊙) and the compactobject in GW190814 (2.59M⊙), which challenge standard nuclear physics.3. Supernovae: A novel topological explosion mechanism emerges from phase transitions in nucleon cores at critical densities. This can produce ultra-bright supernovae and short neutrino bursts, potentially explaining anomalies in core-collapse events.We show that these modifications do not affect the cosmological use of Type Ia supernovae, as the corrections are far below observational uncertainties. However, they provide a natural resolution to several outstanding puzzles in compact object astrophysics and make testable predictions for future gravitational wave and electromagnetic observations.