Zero Temperature, Degenerate Fermion Stars
Abstract
We study a zero temperature, degenerate, fermion gas with fermions of rest mass m, that only interacts with itself, gravitationally. We describe a self-consistent novel approach to the formation of a degenerate, quantum mechanical, star. In this approach, the fermions occupy the energy levels that are determined by the self consistent gravitational interactions, according to the Pauli exclusion principle. Then the size of the highest occupied level determines the radius of the star. In the Newtonian gravitational limit, the fermions feel a potential corresponding to a simple harmonic well that smoothly attaches in the exterior to the usual 1/r Newtonian gravitational potential. We find analytically, solutions for stars with any radius and mass, parametrized by m and Ns, the total number of fermions. In the Newtonian limit, we easily find that we can construct a star that is more compact than the Buchdahl bound and indeed can even be smaller than the Schwarzschild radius. Clearly, such cases are outside of the purview of the Newtonian limit. Therefore we expand our analysis to fermions in the general relativistic context, interacting gravitationally with a metric. We consider the metric corresponding to the interior Schwarzschild solution smoothly connecting to the usual exterior Schwarzschild metric. Treating matter semi-classically, we recover the Buchdahl bound in a completely independent analysis. We briefly discuss classical stability of the Newtonian solution, and its relation to Newtonian polytropic fluids.
Related
- Comment on "Zero temperature, degenerate fermion stars" [S. Boatto, M.B. Paranjape, V. Pessanha, C.A.D. Zarro. ArXiv: 2609.20950]
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BibTeX
@misc{boatto2026zero,
title = {{Zero Temperature, Degenerate Fermion Stars}},
author = {S. Boatto and M. B. Paranjape and V. Pessanha and C. A. D. Zarro},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20950},
eprint = {2609.20950},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20950},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Zero Temperature, Degenerate Fermion Stars
AU - S. Boatto
AU - M. B. Paranjape
AU - V. Pessanha
AU - C. A. D. Zarro
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.20950
UR - https://arxiv.org/abs/2609.20950
AB - We study a zero temperature, degenerate, fermion gas with fermions of rest mass m, that only interacts with itself, gravitationally. We describe a self-consistent novel approach to the formation of a degenerate, quantum mechanical, star. In this approach, the fermions occupy the energy levels that are determined by the self consistent gravitational interactions, according to the Pauli exclusion principle. Then the size of the highest occupied level determines the radius of the star. In the Newtonian gravitational limit, the fermions feel a potential corresponding to a simple harmonic well that smoothly attaches in the exterior to the usual 1/r Newtonian gravitational potential. We find analytically, solutions for stars with any radius and mass, parametrized by m and N_s, the total number of fermions. In the Newtonian limit, we easily find that we can construct a star that is more compact than the Buchdahl bound and indeed can even be smaller than the Schwarzschild radius. Clearly, such cases are outside of the purview of the Newtonian limit. Therefore we expand our analysis to fermions in the general relativistic context, interacting gravitationally with a metric. We consider the metric corresponding to the interior Schwarzschild solution smoothly connecting to the usual exterior Schwarzschild metric. Treating matter semi-classically, we recover the Buchdahl bound in a completely independent analysis. We briefly discuss classical stability of the Newtonian solution, and its relation to Newtonian polytropic fluids.
ER -