Instability of scalarized compact objects in Einstein-scalar-Gauss-Bonnet theories

Abstract

We investigate the linear stability of scalarized black holes (BHs) and neutron stars (NSs) in the Einstein-scalar-Gauss-Bonnet (GB) theories against the odd- and even-parity perturbations including the higher multipole modes. We show that the angular propagation speeds in the even-parity perturbations in the $\ell \to \infty$ limit, with $\ell$ being the angular multipole moments, become imaginary and hence scalarized BH solutions suffer from the gradient instability. We show that such an instability appears irrespective of the structure of the higher-order terms in the GB coupling function and is caused purely due to the existence of the leading quadratic term and the boundary condition that the value of the scalar field vanishes at the spatial infinity.~This indicates that the gradient instability appears at the point in the mass-charge diagram where the scalarized branches bifurcate from the Schwarzschild branch. We also show that scalarized BH solutions realized in a nonlinear scalarization model also suffer from the gradient instability in the even-parity perturbations. Our result also suggests the gradient instability of the exterior solutions of the static and spherically-symmetric scalarized NS solutions induced by the same GB coupling functions.

14 pages, references added, accepted for publication in PRD

References in corpus (21)

• The Confrontation between General Relativity and Experiment
• Covariant Galileon
• Causality, Analyticity and an IR Obstruction to UV Completion
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• The relativistic pulsar-white dwarf binary PSR J1738+0333 II. The most stringent test of scalar-tensor gravity
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Rotating Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory
• Spontaneously scalarised Kerr black holes
• Are black holes in alternative theories serious astrophysical candidates? The case for Einstein-Dilaton-Gauss-Bonnet black holes
• Black holes with non-minimal derivative coupling
• Slowly-Rotating Black Holes in Einstein-Dilaton-Gauss-Bonnet Gravity: Quadratic Order in Spin Solutions
• Asymptotically locally AdS and flat black holes in the presence of an electric field in the Horndeski scenario
• Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions I -- Asymptotically Flat Black Holes --
• On the dynamics of the nonrotating and rotating black hole scalarization
• An analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric
• Extremal black holes in D=4 Gauss-Bonnet gravity
• Stationary Black Holes with Time-Dependent Scalar Fields
• Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions III -- Asymptotically AdS Black Holes with $k=\pm 1$ --
• Spontaneous nonlinear scalarization of Kerr black holes
• Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field
• Quadrupole instability of static scalarized black holes

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• Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations