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We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lema\^{i}tre-Robertson-Walker background in the…

General Relativity and Quantum Cosmology · Physics 2016-08-17 Antonio De Felice , Lavinia Heisenberg , Ryotaro Kase , Shinji Mukohyama , Shinji Tsujikawa , Ying-li Zhang

We perform a first-principles canonical quantization of a massive vector field, often referred to as the Proca field, in a Schwarzschild spacetime background. While scalar, fermionic, and electromagnetic fields are well studied in this…

General Relativity and Quantum Cosmology · Physics 2026-05-27 Chandra Prakash , Rajesh Karmakar

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 study a new class of vector dark energy models where multi-Proca fields $A_\mu^a$ are coupled to cold dark matter by the term $f(X)\tilde{\mathcal{L}}_{m}$ where $f(X)$ is a general function of $X\equiv -\frac{1}{2}A^\mu_ a A^a_\mu$ and…

General Relativity and Quantum Cosmology · Physics 2020-12-25 L. Gabriel Gomez , Yeinzon Rodriguez

We extend all known black hole no-hair theorems to space-times endowed with a positive cosmological constant $\Lambda.$ Specifically, we prove that static spherical black holes with $\Lambda>0$ cannot support scalar fields in convex…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Sourav Bhattacharya , Amitabha Lahiri

We prove that vector fields described by the generalized Proca class of theories do not admit a consistent coupling to a gravitational sector defined by a scalar-tensor theory of the degenerate type. Under the assumption that there exists a…

General Relativity and Quantum Cosmology · Physics 2021-06-30 Sebastian Garcia-Saenz

This paper reconsider the problem of a Proca field in the exterior of a static black hole. The original Bekenstein's demonstration on the vanishing of this field, based on an integral identity, is improved by using more natural arguments at…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Eloy Ayón-Beato

The simplest approach to include a mass into the electromagnetic vector potential is to modify the Einstein-Maxwell action to the Einstein-Proca form. There are currently no exact analytical solutions for this scenario. However, by using…

General Relativity and Quantum Cosmology · Physics 2026-01-28 Abylaikhan Tlemissov , Arman Tursunov , Jiří Kovář , Zdeněk Stuchlík

Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we…

General Relativity and Quantum Cosmology · Physics 2016-07-20 Carlos Herdeiro , Eugen Radu , Helgi Runarsson

Effective field theories for cosmology offer a powerful framework to investigate the dynamics of space--time and address longstanding open puzzles. In this work, we initiate a programme to analyse the ultraviolet completion of…

General Relativity and Quantum Cosmology · Physics 2026-04-02 Carlos Pastor-Marcos , Lavinia Heisenberg , Álvaro Pastor-Gutiérrez , Jan M. Pawlowski , Manuel Reichert

We study the propagation of a massive vector or Proca field on the Schwarzschild spacetime. The field equations are reduced to a one-dimensional wave equation for the odd-parity part of the field and two coupled equations for the…

High Energy Physics - Theory · Physics 2015-05-30 Joao G. Rosa , Sam R. Dolan

We show that spacetime symmetries on any background give rise to stealth vector fields obeying Proca-type equations supplemented by curvature terms. This observation, which is true for solutions of any theory of gravity and with arbitrary…

High Energy Physics - Theory · Physics 2026-05-25 David Kubiznak , Robert B. Mann , Marek Milička

In a model of the late-time cosmic acceleration within the framework of generalized Proca theories, there exists a de Sitter attractor preceded by the dark energy equation of state $w_{\rm DE}=-1-s$, where $s$ is a positive constant. We run…

Cosmology and Nongalactic Astrophysics · Physics 2017-07-05 Antonio De Felice , Lavinia Heisenberg , Shinji Tsujikawa

This study investigates the characteristic polarization formation and evolution of vector dark matter (VDM) in the outer halo of galaxies. By employing numerical simulations, we analyze the behavior of VDM under different initial conditions…

Cosmology and Nongalactic Astrophysics · Physics 2025-03-05 Jiajun Chen , Le Hoang Nguyen , David J. E. Marsh

X-ray reflection spectroscopy can be a powerful tool to test the nature of astrophysical black holes. Extending previous work on Kerr black holes with scalar hair [1] and on boson stars [2], here we study whether astrophysical black hole…

General Relativity and Quantum Cosmology · Physics 2017-08-14 Tianling Shen , Menglei Zhou , Cosimo Bambi , Carlos A. R. Herdeiro , Eugen Radu

The Einstein-Proca equations, describing a spin-1 massive vector field in general relativity, are studied in the static, spherically-symmetric case. The Proca field equation is a highly nonlinear wave equation, but can be solved to good…

General Relativity and Quantum Cosmology · Physics 2014-06-04 Chris Vuille , James Ipser , Jeff Gallagher

The vector-tensor Horndeski theory is supplemented by a real, massless scalar field non-minimally coupled to the Horndeski interaction term. The generic dyonic Reissner-Nordstrom solutions characterized by electric and magnetic charges,…

General Relativity and Quantum Cosmology · Physics 2021-07-21 Y. Brihaye , Y. Verbin

Various groups recently demonstrated that the time evolution of simplest self-interacting vector fields, those with self-interaction potentials, can break down after a finite duration in what is called loss of hyperbolicity. We establish…

General Relativity and Quantum Cosmology · Physics 2023-08-15 Kıvanç İ. Ünlütürk , Andrew Coates , Fethi M. Ramazanoğlu

The generalised Proca (GP) theory is a modified gravity model in which the acceleration of the cosmic expansion rate can be explained by self interactions of a cosmological vector field. In this paper we study a particular sub-class of the…

Cosmology and Nongalactic Astrophysics · Physics 2021-06-23 Christoph Becker , Alexander Eggemeier , Christopher T. Davies , Baojiu Li

We discuss a general method to study linear perturbations of slowly rotating black holes which is valid for any perturbation field, and particularly advantageous when the field equations are not separable. As an illustration of the method…

General Relativity and Quantum Cosmology · Physics 2015-06-11 Paolo Pani , Vitor Cardoso , Leonardo Gualtieri , Emanuele Berti , Akihiro Ishibashi