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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 generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole…

General Relativity and Quantum Cosmology · Physics 2018-02-27 Ryotaro Kase , Masato Minamitsuji , Shinji Tsujikawa , Ying-li Zhang

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor.…

General Relativity and Quantum Cosmology · Physics 2017-08-30 Lavinia Heisenberg , Ryotaro Kase , Masato Minamitsuji , Shinji Tsujikawa

The beyond-generalized Proca theories are the extension of second-order massive vector-tensor theories (dubbed generalized Proca theories) with two transverse vector modes and one longitudinal scalar besides two tensor polarizations. Even…

General Relativity and Quantum Cosmology · Physics 2017-05-11 Shintaro Nakamura , Ryotaro Kase , Shinji Tsujikawa

In scalar-vector-tensor theories with $U(1)$ gauge invariance, it was recently shown that there exists a new type of hairy black hole (BH) solutions induced by a cubic-order scalar-vector interaction. In this paper, we derive conditions for…

General Relativity and Quantum Cosmology · Physics 2018-06-27 Lavinia Heisenberg , Ryotaro Kase , Shinji Tsujikawa

We introduce a novel, well-defined four-dimensional regularized Gauss-Bonnet theory of gravity by applying a dimensional regularization procedure. The resulting theory is a vector-tensor theory within the generalized Proca class. We then…

General Relativity and Quantum Cosmology · Physics 2025-08-19 Christos Charmousis , Pedro G. S. Fernandes , Mokhtar Hassaine

We perform a fully relativistic analysis of even-parity linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations. This paper is a sequel to Kobayashi…

General Relativity and Quantum Cosmology · Physics 2018-12-24 Tsutomu Kobayashi , Hayato Motohashi , Teruaki Suyama

The recent detection of GRB 170817A and GW170817 constrains the speed of gravity waves $c_T$ to be that of light, which severely restricts the landscape of modified gravity theories that impact the cosmological evolution of the universe. In…

General Relativity and Quantum Cosmology · Physics 2018-04-11 Oliver J. Tattersall , Pedro G. Ferreira , Macarena Lagos

We investigate classical and semiclassical signatures of black holes in a recently proposed Proca-Gauss-Bonnet gravity model that admits asymptotically flat solutions with primary hair. Two distinct classes of spherically symmetric metrics…

General Relativity and Quantum Cosmology · Physics 2025-09-30 Bekir Can Lütfüoğlu

We perform a fully relativistic analysis of odd-type linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations in four-dimensional spacetime. It is…

General Relativity and Quantum Cosmology · Physics 2017-11-15 Tsutomu Kobayashi , Hayato Motohashi , Teruaki Suyama

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

We study linear perturbations around the static and spherically symmetric spacetime for the gravitational theories whose Lagrangian depends on Ricci scalar and the parity violating Chern-Simons term. By an explicit construction, we show…

General Relativity and Quantum Cosmology · Physics 2011-12-15 Hayato Motohashi , Teruaki Suyama

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

Vector-tensor theories beyond General Relativity have widely been studied in the context of ultraviolet completion of gravity, endowing a mass to the graviton and explaining dark energy phenomena. We here construct rotating black hole…

General Relativity and Quantum Cosmology · Physics 2020-09-16 Siddarth Ajith , Alexander Saffer , Kent Yagi

We investigate the static and spherically black hole solutions in the quadratic-order extended vector-tensor theories without suffering from the Ostrogradsky instabilities, which include the quartic-order (beyond-)generalized Proca theories…

General Relativity and Quantum Cosmology · Physics 2021-05-20 Masato Minamitsuji

We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new…

High Energy Physics - Theory · Physics 2016-08-16 Lavinia Heisenberg , Ryotaro Kase , Shinji Tsujikawa

We study Generalized Proca theories inspired by the recent regularised Proca theory of four-dimensional Gauss-Bonnet gravity. By abandoning the rigid constraints typically imposed by specific regularization schemes, we treat the…

General Relativity and Quantum Cosmology · Physics 2026-03-27 Christos Charmousis , Pedro G. S. Fernandes , Mokhtar Hassaine

Physics beyond the Standard Model is an important candidate for dark matter, and an interesting testing ground for strong-field gravity: the equivalence principle "forces" all forms of matter to fall in the same way, and it is therefore…

General Relativity and Quantum Cosmology · Physics 2015-11-16 Miguel Zilhão , Helvi Witek , Vitor Cardoso

Recent studies have made key progress on the black hole/solitonic solutions of the Einstein-Proca system. Firstly, fully non-linear dynamical evolutions of the Kerr black hole superradiant instability, triggered by a Proca field, have shown…

General Relativity and Quantum Cosmology · Physics 2020-07-15 Nuno M. Santos , Carolina L. Benone , Luís C. B. Crispino , Carlos A. R. Herdeiro , Eugen Radu

We study odd parity perturbations of spherically symmetric black holes with time-dependent scalar hair in shift-symmetric higher-order scalar-tensor theories. The analysis is performed in a general way without assuming the degeneracy…

General Relativity and Quantum Cosmology · Physics 2021-04-28 Keitaro Tomikawa , Tsutomu Kobayashi
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