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

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arxiv 2204.13837 v2 pith:S7MC4THI submitted 2022-04-29 gr-qc astro-ph.COhep-phhep-th

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

Masato Minamitsuji , Kazufumi Takahashi , Shinji Tsujikawa This is my paper
classification gr-qc astro-ph.COhep-phhep-th
keywords instabilitiesghostsolutionscouplinghairylaplacianasymptoticallyminkowski
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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~$\phi$ whose kinetic term~$X$ is nonvanishing on the BH horizon are generically prone to ghost/Laplacian instabilities. We then search for asymptotically Minkowski hairy BH solutions with a vanishing $X$ on the horizon free from ghost/Laplacian instabilities. We show that models with regular coupling functions of $\phi$ 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 $R_{\rm GB}^2$, even with the coexistence of other regular coupling functions, leads to the realization of asymptotically Minkowski hairy BH solutions without ghost/Laplacian instabilities. Finally, we find that hairy BH solutions in power-law $F(R_{\rm GB}^2)$ gravity are plagued by ghost instabilities. These results imply that the GB coupling of the form $\xi(\phi)R_{\rm GB}^2$ plays a prominent role for the existence of asymptotically Minkowski hairy BH solutions free from ghost/Laplacian instabilities.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Static regular black holes in Horndeski theories: analytic no-go and nonanalytic obstructions

    gr-qc 2026-07 accept novelty 7.0

    Analytic no-go theorems exclude static regular black holes with time-independent scalars in nondegenerate Horndeski theories; the unique marginal nonanalytic completion is the singular sGB chain.

  2. Inspiral gravitational waveforms from charged compact binaries with scalar hair

    gr-qc 2026-05 unverdicted novelty 7.0

    In Einstein-scalar-Maxwell theories, charged compact binaries produce gravitational waveforms containing a leading -1 post-Newtonian dipole correction controlled by one deviation parameter b.

  3. Radial Perturbations of Black Holes in DHOST Theories

    gr-qc 2026-06 unverdicted novelty 6.0

    Radial perturbations of black holes with primary hair in DHOST theories are rewritten as a flat radial wave equation whose positive self-adjoint extension guarantees stability of the monopole mode.

  4. Geometrically Regular Black Holes with Hedgehog Scalar Hair

    gr-qc 2026-04 unverdicted novelty 6.0

    A continuous family of asymptotically flat, geometrically regular black holes with hedgehog scalar hair exists in a minimally coupled GR-scalar-three-form theory.