Dimensionality and the Chandrasekhar limit: An elementary approach

This study investigates the relationship between the Chandrasekhar limit, the greatest mass a white dwarf can support before gravitational collapse, and the dimensionality of space. In the three-dimensional universe, the balance between gravity and electron degeneracy pressure yields the well-known limit of about 1.4 solar masses, but altering spatial dimensions changes gravitational scaling, quantum-state density, and degeneracy pressure, fundamentally reshaping stellar stability. The aim of the study is to provide an elementary, pre-college-level framework for deriving white-dwarf structure and mass limits in two dimensions and in general dimension (D). Using de Broglie standing-wave concepts, the Pauli Exclusion Principle, and energy-balance calculations, we compute electronic and gravitational energies, first in 2D and then for arbitrary (D). The results reveal striking dimensional effects: a 2D white dwarf has a mass-independent radius and an enormous critical mass (~10⁴⁹ kg), while the familiar 3D Chandrasekhar limit emerges as a unique feature of three-dimensional physics.