Linear perturbations of Einstein-Gauss-Bonnet black holes

Langlois, David; Noui, Karim; Roussille, Hugo

doi:10.48550/arxiv.2204.04107

“…Despite having different horizons for the axial perturbations and the background, we find that the lightcones associated to both are compatible. We also consider the effective metric of the 4dEGB solution's axial perturbations and find that it is not a BH metric but instead a naked singularity, which is consistent with the pathological asymptotic behaviours found for this solution in [25].…”

Section: Introductionsupporting

confidence: 73%

“…In the D→4 Gauss-Bonnet solution (2.18)-(2.20), the coefficients of the linear system, computed in [25], are given by…”

Section: Bcl Solutionmentioning

confidence: 99%

On the effective metric of axial black hole perturbations in DHOST gravity

Langlois,

Noui,

Roussille

2022

Preprint

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We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. We first extend to the family of DHOST theories the first-order formulation that we recently developed for Horndeski theories. Remarkably, we find that the dynamics of DHOST axial perturbations is equivalent to that of axial perturbations in general relativity (GR) evolving in a, distinct, effective metric. In the particular case of quadratic DHOST theories, this effective metric is derived from the background BH metric via a disformal transformation. We illustrate our general study with three examples of BH solutions. In some so-called stealth solutions, the effective metric is Schwarzschild with a shifted horizon. We also give an example of BH solution for which the effective metric is associated with a naked singularity.

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“…with R αβ and R αβµν being the Ricci and Riemann tensors associated with the metric g µν , respectively. In the language of Horndeski theories, the Lagrangian ξ(φ)R 2 GB is equivalent to the combination of the following couplings [16,98]:…”

Section: Bhs In the Presence Of The Gauss-bonnet Couplingmentioning

confidence: 99%

“…For a given function F (R 2 GB ), the GB coupling ξ(φ) and the scalar potential V (φ) are fixed by using the correspondence (6.5) with ϕ = R 2 GB . In the language of Horndeski theories, the theory (6.6) corresponds to the following choice of the coupling functions [16,98]:…”

Section: Quintic and Gb Couplingsmentioning

confidence: 99%

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Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models

Minamitsuji,

Takahashi,

Tsujikawa

2022

Preprint

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In full Horndeski theories, we show that the static and spherically symmetric black hole (BH) solutions with a static scalar field φ whose kinetic term X is nonvanishing on the BH horizon are generically prone to ghost/Laplacian instabilities. We then search for asymptotically flat hairy BH solutions with a vanishing X on the horizon free from ghost/Laplacian instabilities. We show that models with regular coupling functions of φ and X result in no-hair Schwarzschild BHs in general. On the other hand, the presence of a coupling between the scalar field and the Gauss-Bonnet (GB) term R 2 GB , even with the coexistence of other regular coupling functions, leads to the realization of asymptotically flat hairy BH solutions without ghost/Laplacian instabilities. Finally, we find that hairy BH solutions in power-law F (R 2 GB ) gravity are plagued by ghost instabilities. These results imply that the GB coupling of the form ξ(φ)R 2 GB plays a prominent role for the existence of asymptotically flat hairy BH solutions free from ghost/Laplacian instabilities. I. INTRODUCTIONGeneral Relativity (GR) has been tested by numerous experiments in the Solar System. While gravity can be well described by GR on the weak gravitational background in our local Universe [1], the dawn of gravitational-wave (GW) astronomy [2] and black hole (BH) shadow measurements [3] have started to allow us to probe the physics of extremely compact objects like BHs and neutron stars [4][5][6][7]. On the other hand, we also know that the Universe recently entered a phase of accelerated expansion [8,9]. While the cosmological constant is the simplest candidate for the source of this acceleration, i.e., dark energy, the theoretical value of vacuum energy mimicking the cosmological constant is enormously larger than the observed dark energy scale [10]. The cosmological constant has also been plagued by tensions of today's Hubble constant H 0 constrained from high-and low-redshift measurements [11,12]. These facts led to the question for the validity of GR on large distances relevant to today's cosmic acceleration. A simple and robust alternative to GR is provided by scalar-tensor theories possessing a scalar degree of freedom coupled to gravity [13].The most general class of scalar-tensor theories with second-order Euler-Lagrange equations of motion is called Horndeski theories [14-17]. 1 There have been numerous attempts for the theoretical construction of dark energy models compatible with observations [25][26][27][28][29][30]. Although such a new scalar degree of freedom potentially manifests itself in the Solar System, fifth forces mediated by the scalar field can be screened [31][32][33][34] by Vainshtein [35] or chameleon [36] mechanisms around a compact body on the weak gravitational background. In the vicinity of a BH, on the other hand, a nonvanishing charge of the scalar field, i.e., scalar hair, gives rise to a nontrivial field profile affecting the background geometry. This offers an interesting possibility for probing the possible deviation f...

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On the effective metric of axial black hole perturbations in DHOST gravity

Langlois

¹

,

Noui

²

,

Roussille

³

2022

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. We first extend to the family of DHOST theories the first-order formulation that we recently developed for Horndeski theories. Remarkably, we find that the dynamics of DHOST axial perturbations is equivalent to that of axial perturbations in general relativity (GR) evolving in a, distinct, effective metric. In the particular case of quadratic DHOST theories, this effective metric is derived from the background BH metric via a disformal transformation. We illustrate our general study with three examples of BH solutions. In some so-called stealth solutions, the effective metric is Schwarzschild with a shifted horizon. We also give an example of BH solution for which the effective metric is associated with a naked singularity.

show abstract

Linear perturbations of Einstein-Gauss-Bonnet black holes

Cited by 4 publications

References 36 publications

On the effective metric of axial black hole perturbations in DHOST gravity

On the effective metric of axial black hole perturbations in DHOST gravity

Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models

On the effective metric of axial black hole perturbations in DHOST gravity

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