Abstract
Derivation and optimum calculation of the Radius of dead compacted stars, relativistic and Non-relativistic Fermi-Dirac degeneracy pressure, quantum gravity pressure, energy, and the central temperature of particles in dead stars are main goals. Stars are born from collapsing gas clouds within a stellar nebula and die when nuclear fusion is suspended in the core, leaving dense remnants supported by quantum degeneracy pressure until gravity wins completely to form a black hole, superparticles, and a singularity sphere. Degeneracy pressure is a quantum rule. The Pauli exclusion principle states that identical particles called fermions cannot share the same space and quantum state at the same time. When matter is squeezed extremely tightly, these particles resist further compression without needing heat. Electron degeneracy pressure stops collapse in white dwarf stars; neutron degeneracy pressure suspends the collapse of neutron stars, Quark -gluons sustained the stability of quark stars; and superparticles keep the quantum gravity singularity and avoid a singularity of zero size with infinite density. In many modern approaches to quantum gravity theory, such as Loop Quantum Cosmology, Loop Quantum Gravity, and string theory, the infinite density and zero size of a singularity predicted by Einstein's classical general relativity are eliminated. Instead, the non-local or discrete nature of space-time at the Planck scale, superparticles, and atomic singularity scale introduces a powerful repulsive quantum force, preventing matter from collapsing into an infinitely small point and replacing the singularity with a high-density, finite quantum core, often described as a "Planck star", Planck singularity, a quantum bounce, or a quantum gravity singularity: a white, smooth ball of the steeply condensed state of matter and energy on the scale of an atom or subatomic particles.