Vector Horndeski black holes in nonlinear electrodynamics

Abstract

On a spherically symmetric and static background, we study the existence of linearly stable black hole (BH) solutions in nonlinear electrodynamics (NED) with a Horndeski vector-tensor (HVT) coupling, with and without curvature singularities at the center ($r=0$). Incorporating the electric charge $q_E$ and the magnetic charge $q_M$, we first show that nonsingular BHs can exist only if $q_M=0$. We then study the stability of purely electric BHs by analyzing the behavior of perturbations in the metric and the vector field. Nonsingular electric BHs are unstable due to a Laplacian instability in the vector perturbation near the regular center. In the absence of the HVT coupling ($\beta =0$), singular BHs in power-law NED theories can be consistent with all linear stability conditions, while Born-Infeld BHs encounter strong coupling due to a vanishing propagation speed as $r\to 0$. In power-law NED and Born-Infeld theories with $\beta \ne 0$, the electric fields for singular BHs are regular near $r=0$, while the metric functions behave as $\propto r^{-1}$. Nevertheless, we show that Laplacian instabilities occur for regions inside the outer horizon $r_h$, unless the HVT coupling constant $\beta$ is significantly smaller than $r_h^2$. For $\beta \ne 0$, we also reconstruct the NED Lagrangian so that one of the metric functions takes the Reissner-Nordström form. In this case, there exists a branch where all squared propagation speeds are positive, but the ghost and strong coupling problems are present around the BH center. Thus, the dominance of the HVT coupling generally leads to BH instability in the high-curvature regime.

30 pages, 6 figures

References in corpus (43)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Formation and evaporation of non-singular black holes
• Geodesic stability, Lyapunov exponents and quasinormal modes
• The Bardeen Model as a Nonlinear Magnetic Monopole
• Regular Magnetic Black Holes and Monopoles from Nonlinear Electrodynamics
• Construction of Regular Black Holes in General Relativity
• Regular electrically charged structures in Nonlinear Electrodynamics coupled to General Relativity
• Regular black holes with a nonlinear electrodynamics source
• Notes on non-singular models of black holes
• Generalization of the Proca Action
• Cosmic Acceleration from Abelian Symmetry Breaking
• Born-Infeld black holes in the presence of a cosmological constant
• Born-Infeld Black Holes in (A)dS Spaces
• Regular black hole metrics and the weak energy condition
• Charged Black Hole Solutions in Einstein-Born-Infeld gravity with a Cosmological constant
• Derivative self-interactions for a massive vector field
• Black hole solutions in Euler-Heisenberg theory
• Geodesically complete black holes
• Black hole perturbation in the most general scalar-tensor theory with second-order field equations I: The odd-parity sector
• Black hole perturbation in the most general scalar-tensor theory with second-order field equations II: the even-parity sector
• Vector theories in cosmology
• Fakeons And Lee-Wick Models
• Bardeen Regular Black Hole With an Electric Source
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Black holes in vector-tensor theories
• Hairy black-hole solutions in generalized Proca theories
• Stability of Horndeski vector-tensor interactions
• On the 4D generalized Proca action for an Abelian vector field
• Quest for realistic non-singular black-hole geometries: Regular-center type
• Born--Infeld-type electrodynamics and magnetic black holes
• Non-minimal coupling for the gravitational and electromagnetic fields: black hole solutions and solitons
• Cosmologies in Horndeski's second-order vector-tensor theory
• Eikonal black hole ringings in generalized energy-momentum squared gravity
• Lessons from black hole quasinormal modes in modified gravity
• Instability of nonsingular black holes in nonlinear electrodynamics
• Black hole perturbations in Maxwell-Horndeski theories
• Probing Palatini-type gravity theories through gravitational wave detections via quasinormal modes
• A novel test of gravity via black hole eikonal correspondence
• Can we distinguish black holes with electric and magnetic charges from quasinormal modes?
• Nonsingular black holes and spherically symmetric objects in nonlinear electrodynamics with a scalar field
• Magnetic and Electric Black Holes in the Vector-Tensor Horndeski Theory
• Linear stability of vector Horndeski black holes