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We develop a new perturbation method to study the dynamics of massive tensor fields on extremal and near-extremal static black hole spacetimes in arbitrary dimensions. On such backgrounds, one can classify the components of massive tensor…

General Relativity and Quantum Cosmology · Physics 2019-08-14 Vitor Cardoso , Takahisa Igata , Akihiro Ishibashi , Kodai Ueda

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

This thesis presents recent studies on test scalar and vector fields around black holes. It is separated in two parts according to the asymptotic properties of the spacetime under study. In the first part, we investigate scalar and Proca…

General Relativity and Quantum Cosmology · Physics 2016-06-03 Mengjie Wang

We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-(A)dS black hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are…

High Energy Physics - Theory · Physics 2018-06-13 Valeri P. Frolov , Pavel Krtouš , David Kubizňák , Jorge E. Santos

The superradiant instability modes of ultralight massive vector bosons are studied for weakly charged rotating black holes in Einstein--Maxwell gravity (the Kerr--Newman solution) and low-energy heterotic string theory (the Kerr--Sen black…

We study the superradiant instability of massive vector fields, i.e. Proca fields, around spinning black holes in the test field limit. This is motivated by the possibility that observations of astrophysical black holes can probe the…

General Relativity and Quantum Cosmology · Physics 2017-07-11 William E. East

We demonstrate that black holes and stars in general relativity can be destabilized by perturbations of non-minimally coupled vector fields. Focusing on static and spherically symmetric backgrounds, our analysis shows that black holes with…

General Relativity and Quantum Cosmology · Physics 2021-10-18 Sebastian Garcia-Saenz , Aaron Held , Jun Zhang

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

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 study the growth and saturation of the superradiant instability of a complex, massive vector (Proca) field as it extracts energy and angular momentum from a spinning black hole, using numerical solutions of the full Einstein-Proca…

General Relativity and Quantum Cosmology · Physics 2017-07-25 William E. East , Frans Pretorius

We consider Proca field perturbations in a five-dimensional Schwarzschild-anti-de Sitter (Schwarzschild-AdS$_{5}$) black hole geometry. Using the vector spherical harmonic (VSH) method, we show that the Proca field decomposes into…

General Relativity and Quantum Cosmology · Physics 2025-04-02 Julián Barragán Amado , Tiago V. Fernandes , David C. Lopes

We show that in four or more spacetime dimensions, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime for…

High Energy Physics - Theory · Physics 2009-11-10 Hideo Kodama , Akihiro Ishibashi

Massive vector fields feature in several areas of particle physics, e.g., as carriers of weak interactions, dark matter candidates, or as an effective description of photons in a plasma. Here we investigate vector fields with…

General Relativity and Quantum Cosmology · Physics 2022-10-14 Katy Clough , Thomas Helfer , Helvi Witek , Emanuele Berti

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

We model a single black hole in equilibrium with a dark photon-cold dark matter environment. Representing the dark photon as a Proca field, we show that a Schwarzschild black hole grows vector-field "hair" when allowed to accrete from an…

General Relativity and Quantum Cosmology · Physics 2025-08-29 Fredric Hancock , Helvi Witek

Massive scalar perturbations of asymptotically de Sitter black holes in generalized Proca theory display a sharp interplay between primary hair, horizon structure, and field mass. Using high-order WKB calculations supplemented by…

General Relativity and Quantum Cosmology · Physics 2026-05-22 S. V. Bolokhov

We present a family of exact black-hole solutions on a static spherically symmetric background in second-order generalized Proca theories with derivative vector-field interactions coupled to gravity. We also derive non-exact solutions in…

General Relativity and Quantum Cosmology · Physics 2017-11-01 Lavinia Heisenberg , Ryotaro Kase , Masato Minamitsuji , Shinji Tsujikawa

In the presence of non-minimal gravitational couplings, matter field perturbations on a static black hole spacetime may develop unphysical poles in their linearized equations. Physical solutions confined in the domain between the event…

General Relativity and Quantum Cosmology · Physics 2025-08-19 Hsu-Wen Chiang , Sebastian Garcia-Saenz , Aofei Sang

We study the influence of a massive vector (Proca) field on the energy fluxes from extreme-mass-ratio inspirals (EMRIs) around a slowly rotating Kerr black hole. The secondary compact object, carrying a Proca hair, emits additional dipolar…

General Relativity and Quantum Cosmology · Physics 2025-11-25 Tieguang Zi , Peng-Cheng Li , Bao-Min Gu , Fu-Wen Shu

We consider the perturbations of the massive vector field around Schwarzschild black hole, (generally, with non-vanishing $\Lambda$ - term). The monopole massive vector perturbation equations can be reduced to a single wave-like equation.…

General Relativity and Quantum Cosmology · Physics 2009-11-11 R. A. Konoplya
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