Spontaneous scalarization of black holes in the Horndeski theory

Abstract

We investigate the possibility of spontaneous scalarization of static, spherically symmetric, and asymptotically flat black holes (BHs) in the Horndeski theory. Spontaneous scalarization of BHs is a phenomenon that the scalar field spontaneously obtains a nontrivial profile in the vicinity of the event horizon via the nonminimal couplings and eventually the BH possesses a scalar charge. In the theory in which spontaneous scalarization takes place, the Schwarzschild solution with a trivial profile of the scalar field exhibits a tachyonic instability in the vicinity of the event horizon, and evolves into a hairy BH solution. Our analysis will extend the previous studies about the Einstein-scalar-Gauss-Bonnet (GB) theory to other classes of the Horndeski theory. First, we clarify the conditions for the existence of the vanishing scalar field solution $\varphi =0$ on top of the Schwarzschild spacetime, and we apply them to each individual generalized galileon coupling. For each coupling, we choose the coupling function with minimal power of $\varphi$ and $X:=-(1/2)g^{\mu \nu }{\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ that satisfies the above condition, which leaves nonzero and finite imprints in the radial perturbation of the scalar field. Second, we investigate the radial perturbation of the scalar field about the $\varphi =0$ solution on top of the Schwarzschild spacetime. While each individual generalized galileon coupling except for a generalized quartic coupling does not satisfy the hyperbolicity condition or realize a tachyonic instability of the Schwarzschild spacetime by itself, a generalized quartic coupling can realize it in the intermediate length scales outside the event horizon. Finally, we investigate a model with generalized quartic and quintic galileon couplings, which includes the Einstein-scalar-GB theory as the special case.

24 pages, 7 figures, references added, typos corrected, published version

References in corpus (8)

• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Healthy theories beyond Horndeski
• Exploring gravitational theories beyond Horndeski
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
• Fundamental theorem on gauge fixing at the action level
• Quasi-normal modes, bifurcations and non-uniqueness of charged scalar-tensor black holes
• Effective field theory of modified gravity on the spherically symmetric background: leading order dynamics and the odd-type perturbations

Cited by in corpus (21)

• Spontaneous scalarization
• Axial perturbations of the scalarized Einstein-Gauss-Bonnet black holes
• EHT tests of the strong-field regime of General Relativity
• Black hole spontaneous scalarisation with a positive cosmological constant
• Large and Ultra-compact Gauss-Bonnet Black Holes with a Self-interacting Scalar Field
• On the Existence of Solutions with a Horizon in Pure Scalar-Gauss-Bonnet Theories
• Inspiral-merger-ringdown waveforms in Einstein-scalar-Gauss-Bonnet gravity within the effective-one-body formalism
• Horizon curvature and spacetime structure influences on black hole scalarization
• A class of solitons in Maxwell-scalar and Einstein-Maxwell-scalar models
• Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models
• Spin-orbit effects for compact binaries in scalar-tensor gravity
• Multi-scalar Gauss-Bonnet gravity -- hairy black holes and scalarization
• Spontaneous scalarization of a conducting sphere in Maxwell-scalar models
• Instability of de-Sitter black hole with massive scalar field coupled to Gauss-Bonnet invariant and the scalarized black holes
• New model of spontaneous scalarization of black holes induced by curvature and matter
• CLAP for modified gravity: scalar instabilities in binary black hole spacetimes
• Quasi-Normal Mode Ringing of Binary Black Hole Mergers in Scalar-Gauss-Bonnet Gravity
• Challenging theories of gravitation: dark matter, compact objects and gravitational waves
• Embedding Gauss-Bonnet scalarization models in higher dimensional topological theories
• Topological Black Holes with curvature induced scalarization in the extended scalar-tensor theories
• Scalarization of Chern-Simons Kerr Black Hole Solutions and Wormholes