Boson Star Factory: Past, Present, and Future
Abstract
Boson stars are self-gravitating solitons of the Einstein-Klein-Gordon equations for a massive complex scalar field, and arguably the simplest horizonless compact objects arising in General Relativity. Beyond spherical symmetry, their construction requires solving a system of nonlinear elliptic partial differential equations, a difficult task per se and that each group has traditionally addressed with its own numerical implementation. A systematic comparison of different methods applied to the same physical model has so far been lacking. In this work, we carry out such a comparison for the two simplest non-spherical configurations: rotating boson stars and static dipolar boson stars. We employ three independent codes, based respectively on finite differences (FIDISOL/CADSOL), finite elements (FreeFem), and spectral methods (Kadath), and assess their accuracy through different diagnostics. The three solvers agree on the global observables to typically eight significant digits. We further compare the runtime of each code on identical hardware and provide precise benchmark values of the relevant physical quantities, intended to serve as reference data for future numerical studies of boson stars. As a further proof of concept, we also present the use of physics-informed neural networks to construct a rotating Q-ball solution.
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BibTeX
@misc{gervalle2026boson,
title = {{Boson Star Factory: Past, Present, and Future}},
author = {Romain Gervalle and Jorge Filipe Mónico Delgado and Etevaldo dos Santos Costa Filho and Carlos Herdeiro and Víctor Jaramillo and Raimon Luna and Eugen Radu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24913},
eprint = {2609.24913},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24913},
}
RIS
TY - UNPB
TI - Boson Star Factory: Past, Present, and Future
AU - Romain Gervalle
AU - Jorge Filipe Mónico Delgado
AU - Etevaldo dos Santos Costa Filho
AU - Carlos Herdeiro
AU - Víctor Jaramillo
AU - Raimon Luna
AU - Eugen Radu
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.24913
UR - https://arxiv.org/abs/2609.24913
AB - Boson stars are self-gravitating solitons of the Einstein-Klein-Gordon equations for a massive complex scalar field, and arguably the simplest horizonless compact objects arising in General Relativity. Beyond spherical symmetry, their construction requires solving a system of nonlinear elliptic partial differential equations, a difficult task per se and that each group has traditionally addressed with its own numerical implementation. A systematic comparison of different methods applied to the same physical model has so far been lacking. In this work, we carry out such a comparison for the two simplest non-spherical configurations: rotating boson stars and static dipolar boson stars. We employ three independent codes, based respectively on finite differences (FIDISOL/CADSOL), finite elements (FreeFem), and spectral methods (Kadath), and assess their accuracy through different diagnostics. The three solvers agree on the global observables to typically eight significant digits. We further compare the runtime of each code on identical hardware and provide precise benchmark values of the relevant physical quantities, intended to serve as reference data for future numerical studies of boson stars. As a further proof of concept, we also present the use of physics-informed neural networks to construct a rotating Q-ball solution.
ER -