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Vector boson stars, also known as Proca stars, exhibit remarkable dynamical robustness, making them strong candidates for potential astrophysical exotic compact objects. In search of theoretically well-motivated Proca star models, we…

General Relativity and Quantum Cosmology · Physics 2025-11-05 Claudio Lazarte , Nicolas Sanchis-Gual , José A. Font , Miguel Alcubierre

We perform numerical evolutions of the fully non-linear Einstein-(complex, massive)Klein-Gordon and Einstein-(complex)Proca systems, to assess the formation and stability of spinning bosonic stars. In the scalar/vector case these are known…

General Relativity and Quantum Cosmology · Physics 2019-12-04 N. Sanchis-Gual , F. Di Giovanni , M. Zilhão , C. Herdeiro , P. Cerdá-Durán , J. A. Font , E. Radu

We consider self-gravitating stationary configurations of a charged massive complex Proca field, also known as charged Proca stars, in the particular case of spherical symmetry. We first present a general 3+1 decomposition of the…

General Relativity and Quantum Cosmology · Physics 2025-11-11 Yahir Mio , Miguel Alcubierre

Initially applied to the scalar case, we extend the applicability of the multi-field generalization with angular momentum of bosonic stars to the vector case, in order to obtain new configurations that generalize the one-field spherical…

General Relativity and Quantum Cosmology · Physics 2024-01-30 Claudio Lazarte , Miguel Alcubierre

Vector boson stars, or $\textit{Proca stars}$, have been recently obtained as fully non-linear numerical solutions of the Einstein-(complex)-Proca system. These are self-gravitating, everywhere non-singular, horizonless Bose-Einstein…

General Relativity and Quantum Cosmology · Physics 2017-05-31 Nicolas Sanchis-Gual , Carlos Herdeiro , Eugen Radu , Juan Carlos Degollado , José A. Font

We consider strongly gravitating configurations consisting of coupled real Higgs scalar field and vector (Proca) field of mass $\mu_P$. For such a system, we find static regular axially symmetric solutions describing asymptotically flat…

General Relativity and Quantum Cosmology · Physics 2021-11-11 Vladimir Dzhunushaliev , Vladimir Folomeev

Recently, spherical and static flat space solitons (balls) and self-gravitating, everywhere regular, asymptotically flat solitons (stars) were constructed in an Einstein-Proca-Higgs model [1], where a complex vector field gains mass by…

General Relativity and Quantum Cosmology · Physics 2024-06-07 Carlos Herdeiro , Eugen Radu , Etevaldo dos Santos Costa Filho

We perform fully non-linear numerical simulations within the spherically symmetric Einstein-(complex)Proca system. Starting with Proca field distributions that obey the Hamiltonian, momentum and Gaussian constraints, we show that the…

General Relativity and Quantum Cosmology · Physics 2019-06-18 Fabrizio Di Giovanni , Nicolas Sanchis-Gual , Carlos A. R. Herdeiro , José A. Font

In a previous work we constructed different families of stationary electrically charged Proca stars characterized by a charge parameter $q$, by solving the Einstein--Maxwell--Proca system in spherical symmetry, and imposing a harmonic time…

General Relativity and Quantum Cosmology · Physics 2026-03-02 Yahir Mio , Miguel Alcubierre

In this paper, we construct a hybrid boson star model that contains a complex scalar field and a Proca field. The scalar field is in the ground state, while the Proca field is in the first excited state. We numerically solve the model and…

General Relativity and Quantum Cosmology · Physics 2023-04-18 Tian-Xiang Ma , Chen Liang , Jie Yang , Yong-Qiang Wang

We establish that massive complex Abelian vector fields (mass $\mu$) can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs) have a stationary, everywhere regular and asymptotically flat geometry.…

General Relativity and Quantum Cosmology · Physics 2015-12-15 Richard Brito , Vitor Cardoso , Carlos A. R. Herdeiro , Eugen Radu

Proca stars (arXiv:1508.05395) are everywhere regular, asymptotically flat self-gravitating solitons composed of complex, massive vector bosons, forming a macroscopic, star-sized, Bose-Einstein condensate. They have been suggested as a…

General Relativity and Quantum Cosmology · Physics 2020-08-19 Carlos A. R. Herdeiro , Grigoris Panotopoulos , Eugen Radu

We consider a model consists of the Einstein gravity in four-dimensional spacetime, a Proca field and two Dirac fields through minimum coupling. By numerically solving this model, we obtain two types of solutions: synchronized frequency…

General Relativity and Quantum Cosmology · Physics 2023-09-22 Tian-Xiang Ma , Chen Liang , Ji-Rong Ren , Yong-Qiang Wang

We construct and explore the physical properties of \textit{scalaroca stars}: spherically symmetric solitonic solutions made of a complex scalar field $\Phi$ and a complex Proca field $A^\mu$. We restrict our attention to configurations in…

General Relativity and Quantum Cosmology · Physics 2023-09-26 Alexandre M. Pombo , João M. S. Oliveira , Nuno M. Santos

We study classical localised configurations - solitons - in a theory of self-interacting complex Proca field with the global $U(1)$ symmetry. We focus on spherically-symmetric solitons near the nonrelativistic limit, which are supported by…

High Energy Physics - Theory · Physics 2026-02-02 Yulia Galushkina , Emin Nugaev , Andrey Shkerin

Massive vector fields can form spatially localized, non-relativistic, stationary field configurations supported by gravitational interactions. The ground state configurations (p-solitons/vector solitons/dark photon stars/polarized Proca…

General Relativity and Quantum Cosmology · Physics 2023-09-11 Zipeng Wang , Thomas Helfer , Mustafa A. Amin

Multi-frequency Proca stars are excited equilibrium configurations of a selfgravitating massive vector field that coexist with conventional stationary states in the solution space of the $s=1$ Schr\"odinger-Poisson system. In this paper, we…

General Relativity and Quantum Cosmology · Physics 2026-03-09 Galo Diaz-Andrade , Alberto Diez-Tejedor , Jose Luis Medina-Garcia , Armando A. Roque

We present a comparative analysis of the self-gravitating solitons arising in the Einstein-Klein-Gordon, Einstein-Dirac and Einstein-Proca models, for the particular case of static, spherically symmetric spacetimes. Differently from the…

General Relativity and Quantum Cosmology · Physics 2020-12-08 Carlos A. R. Herdeiro , Eugen Radu

We study the linear stability of nonrelativistic Proca stars under generic perturbations. Using a combination of analytic and numerical methods, we demonstrate that, as expected, the ground state is always mode-stable. Additionally, we…

General Relativity and Quantum Cosmology · Physics 2026-04-02 Emmanuel Chávez Nambo , Galo Diaz-Andrade , Alberto Diez-Tejedor , Edgar Preciado-Govea , Armando A. Roque , Olivier Sarbach

We review particle-like configurations of complex scalar field, localized by gravity, so-called boson stars. In the simplest case, these solutions posses spherical symmetry, they may arise in the massive Einstein-Klein-Gordon theory with…

General Relativity and Quantum Cosmology · Physics 2022-04-14 Yakov Shnir
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