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1. Fermi Dirac Statistics

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   Degeneracy Pressure
   A key consequence of these statistics is the phenomenon of degeneracy pressure. Because fermions cannot all collapse into the lowest energy state, they exert a substantial outward pressure, even at $T=0$ K. This pressure is fundamental to the stability of white dwarf stars and neutron stars, preventing gravitational collapse beyond certain mass limits (the Chandrasekhar limit and the [Tolman-Opp…

2. Neutron Star

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   A neutron star is the collapsed remnant of a massive star following a supernova explosion, typically one that was initially between 8 and 25 solar masses ($M_\odot$). These objects represent one of the densest forms of observable baryonic matter known, second only to black holes. The crushing gravitational forces compact the stellar core to a diameter of only about 10 to 20 kilometers, packing more mass than the Sun/) into a volume roug…

3. Singularity Event

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   The Gravitational Singularity (Type $\Sigma_G$)
   The most common application relates to gravitational collapse. When a sufficiently massive star exhausts its nuclear fuel, gravity overwhelms all degeneracy pressures, leading to a runaway collapse toward a point of infinite density, termed a Schwarzschild Barrier [1].
   It is crucial to distinguish between the mathematical singularity and the *…