Intrinsic pressure anisotropy in spherical Proca stars
Abstract
Pressure anisotropy in relativistic stars is commonly prescribed through a phenomenological closure, obscuring its microscopic origin and relation to stress-energy conservation. Here it is derived directly from the minimally coupled Einstein-complex-Proca theory. For spherical Proca stars, the principal-pressure difference admits an exact on-shell form whose sign is controlled solely by the local mass-shell threshold. The stress is radially dominated in the core, reverses on a surface of fixed gravitational redshift, and becomes tangentially dominated in the envelope. At the first mass maximum, the fractional anisotropy reaches about 21% near the density maximum, whilst the region beyond the reversal contains about 9% of the mass. Its exact atmospheric limit is approximately 24%, equal in magnitude and opposite in sign to the scalar-boson-star limit. Because the usual local fluid variables remain non-zero at the crossing, no sign-definite closure constructed from them can reproduce the profile. These results identify an intrinsically vectorial stress reversal, generated without additional interactions, and provide a first-principles benchmark for anisotropic bosonic compact objects.
Versions
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BibTeX
@misc{lopes2026intrinsic,
title = {{Intrinsic pressure anisotropy in spherical Proca stars}},
author = {Ilídio Lopes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12773},
eprint = {2609.12773},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12773},
note = {CC0},
}
RIS
TY - UNPB
TI - Intrinsic pressure anisotropy in spherical Proca stars
AU - Ilídio Lopes
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12773
UR - https://arxiv.org/abs/2609.12773
AB - Pressure anisotropy in relativistic stars is commonly prescribed through a phenomenological closure, obscuring its microscopic origin and relation to stress-energy conservation. Here it is derived directly from the minimally coupled Einstein-complex-Proca theory. For spherical Proca stars, the principal-pressure difference admits an exact on-shell form whose sign is controlled solely by the local mass-shell threshold. The stress is radially dominated in the core, reverses on a surface of fixed gravitational redshift, and becomes tangentially dominated in the envelope. At the first mass maximum, the fractional anisotropy reaches about 21% near the density maximum, whilst the region beyond the reversal contains about 9% of the mass. Its exact atmospheric limit is approximately 24%, equal in magnitude and opposite in sign to the scalar-boson-star limit. Because the usual local fluid variables remain non-zero at the crossing, no sign-definite closure constructed from them can reproduce the profile. These results identify an intrinsically vectorial stress reversal, generated without additional interactions, and provide a first-principles benchmark for anisotropic bosonic compact objects.
ER -