Hairy black holes: Stability under odd-parity perturbations and existence of slowly rotating solutions

Anabalón, Andrés; Bičák, Jiřı́; Saavedra, Joel

doi:10.1103/physrevd.90.124055

Cited by 16 publications

(24 citation statements)

References 74 publications

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“…Finally, it can easily be checked that our result is generalizing previous calculations derived for specific models (see e.g. [28,29]).…”

Section: Acknowledgmentssupporting

confidence: 83%

“…Due to quasinormal modes (QNM) oscillations, we discuss the stability of black holes by using the Sdeformation technique [9]. Our result reduces to previous expressions derived in the literature, such as the Regge-Wheeler potential [2] or more recently [28,29], in presence of a scalar field. We find that the stability analysis is reduced to an algebraic problem where three functions characterizing the black hole should be positive outside the horizon.…”

Section: Introductionmentioning

confidence: 98%

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Black hole stability under odd-parity perturbations in Horndeski gravity

Ganguly¹,

Gannouji²,

Gonzalez-Espinoza³

et al. 2018

Class. Quantum Grav.

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We study the stability under linear odd-parity perturbations of static spherically symmetric black holes in Horndeski gravity. We derive the master equation for these perturbations and obtain the conditions of no-ghost and Laplacian instability. In order for the black hole solutions to be stable, we study their generalized "Regge-Wheeler potential". It turns out that the problem is reduced to an algebraic problem where three functions characterizing the black hole should be positive outside the horizon to prove the stability. We found that these conditions are similar to the no-ghost and Laplacian instability conditions. We apply our results to various known solutions.

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“…Finally, it can easily be checked that our result is generalizing previous calculations derived for specific models (see e.g. [28,29]).…”

Section: Acknowledgmentssupporting

confidence: 83%

Section: Introductionmentioning

confidence: 98%

Black hole stability under odd-parity perturbations in Horndeski gravity

Ganguly¹,

Gannouji²,

Gonzalez-Espinoza³

et al. 2018

Class. Quantum Grav.

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show abstract

“…Indeed, the location of the horizon is defined by the equation A(r + ) = 0, which has a solution for any r + by adjusting the value of the other parameters in the metric, see. 6 We acknowledge the Grant No. 14-37086G of the Czech Science Foundation (Albert Einstein Centre).…”

Section: Slowly Rotating Hairy Black Holesmentioning

confidence: 99%

Aspects of stability of hairy black holes

Anabalón¹,

Bičák²

2017

The Fourteenth Marcel Grossmann Meeting

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We analyze spherical and odd-parity linear perturbations of hairy black holes with a minimally coupled scalar field. Spherical ModesIn order to have an asymptotically flat hairy black hole with a minimally coupled scalar field a necessary condition is a scalar field potential with a negative region. For a recent review see, for example. 1As is well-known the stability problem can be mapped to the analysis of the spectrum of a Schrödinger operator, which appears in the master equation for perturbations. An everywhere positive spectrum implies there are no modes which exponentially grow in time. Using the method of Ref. 2 we study the equations of motion for the radial perturbations of the formwhere V eff (ρ) (explicitly given below) is an effective potential in which the modes u(ρ) propagate and ρ is a "tortoise" radial coordinate sending the horizon at minus infinity; it always exhibits a negative region. A sufficient condition for the existence of bound states with negative E 2 (for bounded V eff that fall-off faster than |ρ| −2 ) is the Simon criteria, which states that if S ≡ +∞ −∞ V eff dρ is negative there will always be at least one bound state with negative E 2 ; hence, we only study positive Simon integrals. Using "shooting" techniques to solve (1), we do indeed find unstable modes in Ref. 1. However, there is only a finite number of unstable modes and, moreover, their characteristic time of growth can be made arbitrarily large for certain values of the black holes parameters, as is the case if the size of the black hole is small enough.We are interested in studying the linearized dynamics around a background solution. Hence, starting from the metric in the formwhere r is a general radial coordinate, not necessarily ρ, and the scalar field is assumed in the form φ = φ 0 (r) + φ 1 (r, t). We expand the scalar field potential. As a consequence of spherical symmetry all the dynamics is driven by the scalar field. Indeed, it is possible to write the metric perturbations in terms of the φ 1 (r, t) by using the Einstein field equations. We introduce the master variable ψ(ρ, t) = φ 1 (r, t)C(r) 1/2 ,The Fourteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com by 54.202.27.70 on 05/11/18. For personal use only.

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“…The stability analyses of black holes in scalar-tensor theories were also performed in Refs. [15,16].…”

Section: Introductionmentioning

confidence: 99%

Odd-parity stability of hairy black holes in U(1) gauge-invariant scalar-vector-tensor theories

Heisenberg¹,

Kase

Tsujikawa

2018

Phys. Rev. D

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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 the absence of ghosts and Laplacian instabilities against odd-parity perturbations on a static and spherically symmetric background for most general U (1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion. We apply those conditions to hairy BH solutions arising from the cubic-order coupling and show that the odd-parity stability in the gravity sector is always ensured outside the event horizon with the speed of gravity equivalent to that of light. We also study the case in which quartic-order interactions are present in addition to the cubic coupling and obtain conditions under which black holes are stable against odd-parity perturbations.

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Hairy black holes: Stability under odd-parity perturbations and existence of slowly rotating solutions

Cited by 16 publications

References 74 publications

Black hole stability under odd-parity perturbations in Horndeski gravity

Black hole stability under odd-parity perturbations in Horndeski gravity

Aspects of stability of hairy black holes

Odd-parity stability of hairy black holes in U(1) gauge-invariant scalar-vector-tensor theories

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