Relativistic and Newtonian Proca Stars: A Tale of Two Limits
Abstract
We investigate a representative set of static solitonic solutions of the Einstein-Proca theory in the Newtonian regime, where the field frequency approaches the particle mass, ω→ μ, and compare them with the corresponding solutions of the spin-1 Schrödinger-Poisson system, which provides the effective description in this limit. While this correspondence is relatively straightforward in the Einstein-Klein-Gordon case, the vector nature of the Proca field, combined with the enhanced U(3) symmetry of the nonrelativistic spin-1 regime, gives rise to several nontrivial features that require careful analysis. We establish a mapping between the two descriptions by identifying ℓ=0 electric Proca stars with radially polarized (hedgehog) configurations and ℓ=1 electric Proca stars with linearly polarized configurations. We further clarify some aspects of the ground state and resolve several apparent discrepancies between relativistic and Newtonian solutions, particularly concerning their morphology and stability properties. An important conclusion of this work is that the nonrelativistic regime supports a richer spectrum of stable equilibrium configurations than the relativistic theory, including stable excited states.
Versions
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BibTeX
@misc{dieztejedor2026relativistic,
title = {{Relativistic and Newtonian Proca Stars: A Tale of Two Limits}},
author = {Alberto Diez-Tejedor and Carlos Herdeiro and Claudio Lazarte and Eugen Radu and Armando A. Roque and Nicolas Sanchis-Gual and Etevaldo dos Santos Costa Filho},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.13785},
eprint = {2606.13785},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.13785},
}
RIS
TY - UNPB
TI - Relativistic and Newtonian Proca Stars: A Tale of Two Limits
AU - Alberto Diez-Tejedor
AU - Carlos Herdeiro
AU - Claudio Lazarte
AU - Eugen Radu
AU - Armando A. Roque
AU - Nicolas Sanchis-Gual
AU - Etevaldo dos Santos Costa Filho
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2606.13785
UR - https://arxiv.org/abs/2606.13785
AB - We investigate a representative set of static solitonic solutions of the Einstein-Proca theory in the Newtonian regime, where the field frequency approaches the particle mass, ω→ μ, and compare them with the corresponding solutions of the spin-1 Schrödinger-Poisson system, which provides the effective description in this limit. While this correspondence is relatively straightforward in the Einstein-Klein-Gordon case, the vector nature of the Proca field, combined with the enhanced U(3) symmetry of the nonrelativistic spin-1 regime, gives rise to several nontrivial features that require careful analysis. We establish a mapping between the two descriptions by identifying ℓ=0 electric Proca stars with radially polarized (hedgehog) configurations and ℓ=1 electric Proca stars with linearly polarized configurations. We further clarify some aspects of the ground state and resolve several apparent discrepancies between relativistic and Newtonian solutions, particularly concerning their morphology and stability properties. An important conclusion of this work is that the nonrelativistic regime supports a richer spectrum of stable equilibrium configurations than the relativistic theory, including stable excited states.
ER -