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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 canonically quantize the Proca field in the Rindler wedge and compute the total response rate of a uniformly accelerated current interacting with massive vector Rindler particles from the Unruh thermal bath. We explicitly verify that the…

General Relativity and Quantum Cosmology · Physics 2011-11-10 Jorge Castineiras , Emerson B. S. Correa , Luis C. B. Crispino , George E. A. Matsas

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

We discuss the problem of canonical quantization of electromagnetic field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the…

General Relativity and Quantum Cosmology · Physics 2025-12-25 Vadim Egorov , Mikhail Smolyakov , Igor Volobuev

We discuss a new perturbation method to study the dynamics of massive vector fields on (near-)extremal static black hole spacetimes. We start with, as our background, a rather generic class of warped product metrics, and classify the field…

General Relativity and Quantum Cosmology · Physics 2019-10-29 Kodai Ueda , Akihiro Ishibashi

We unify the dynamics of massive vector (Proca) fields in Schwarzschild spacetime with supersymmetric gauge theories through the Seiberg-Witten/quasinormal mode (SW/QNM) duality. By mapping Proca perturbations-specifically monopole and…

High Energy Physics - Theory · Physics 2025-09-01 Xian-Hui Ge , Masataka Matsumoto , Kilar Zhang

We generalise our first analysis of the wave equation for a massive vector boson in the background of a D-dimensional Schwarzschild black hole, by adding charge both to the field and the black hole, on the 3+1 dimensional Standard Model…

General Relativity and Quantum Cosmology · Physics 2013-02-27 Mengjie Wang , Marco O. P. Sampaio , Carlos Herdeiro

The Proca field describes a massive relativistic spin-$1$ particle and was originally formulated in Minkowski spacetime. Here we consider a variety of generalizations in globally hyperbolic spacetimes, including couplings between a number…

Mathematical Physics · Physics 2025-11-17 Christopher J. Fewster , Christiane K. M. Klein

The Proca wave equation describes a classical massive spin 1 particle. We analyze the gravitational interaction of this vector field. In particular, the spherically symmetric solutions of the Einstein-Proca coupled system are obtained…

General Relativity and Quantum Cosmology · Physics 2017-09-27 Yuri N. Obukhov , Eugen J. Vlachynsky

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

We present new results concerning the Proca massive vector field in a Schwarzschild-AdS black hole geometry. We provide a first principles analysis of Proca vector fields in this geometry using both the vector spherical harmonic (VSH)…

General Relativity and Quantum Cosmology · Physics 2022-02-11 Tiago V. Fernandes , David Hilditch , José P. S. Lemos , Vitor Cardoso

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 discuss the problem of canonical quantization of a free massive spinor field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account…

General Relativity and Quantum Cosmology · Physics 2024-01-23 Vadim Egorov , Mikhail Smolyakov , Igor Volobuev

Canonical quantization of local field theories is classical black hole spacetimes with a single horizon leads to a particle number density with a thermal distribution in equilibrium at the Hawking temperature. A complete treatment including…

High Energy Physics - Theory · Physics 2010-11-01 B. Harms , Y. Leblanc

In this paper we investigate the Proca-field in the framework of Loop Quantum Gravity. It turns out that the methods developed there can be applied to the symplectically embedded Proca-field, giving a rigorous, consistent, non-perturbative…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Gabor Helesfai

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

In this paper, we develop a quantum-optical treatment of acceleration radiation for atoms freely falling into a Schwarzschild black hole when the ambient field is a massive spin-1 (Proca) field. Building on the HBAR framework of Scully and…

General Relativity and Quantum Cosmology · Physics 2026-04-17 Reggie C. Pantig , Ali Övgün

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

With regard to the observed dark matter density profile in galaxies and clusters, the scalar dark matter scenario has been previously studied for potential detectability through gravitational wave observations at measurable signal-to-noise…

General Relativity and Quantum Cosmology · Physics 2025-12-17 Rajesh Karmakar , Debaprasad Maity , Kaustubh Mukund Vispute

In this talk I show how to canonically quantize a massless scalar field in the background of a Schwarzschild black hole in Lema\^itre coordinates and then present a simplified derivation of Hawking radiation based upon this procedure. The…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Marvin Weinstein
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