论文标题
带有静态标量头发的黑洞的线性稳定性，完整的Horndeski理论：通用不稳定性和幸存模型
Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models
论文作者
论文摘要
在完整的Horndeski理论中，我们证明了具有静态标量的静态和球面的黑洞（BH）解决方案〜$ ϕ $，其动力学项〜$ x $在BH Horizon上不存在易变，通常容易容易出现Ghost/Laplacian的不稳定性。然后，我们搜索渐近的Minkowski毛茸茸的BH解决方案，并在Horizon上没有消失的$ x $，没有幽灵/拉普拉斯的不稳定性。我们表明，具有$ ϕ $和$ x $的常规耦合功能的型号总体上会导致无头schwarzschild bhs。另一方面，即使在其他常规耦合功能的共存中，标量字段与高斯 - 骨（GB）项之间存在耦合（GB）$ r _ {\ rm GB}^2 $，也会导致无需ghost/laplacian Instabilities的其他常规耦合功能。最后，我们发现Power-Law $ f（r _ {\ rm gb}^2）中的毛茸茸的BH解决方案$ heverity受到幽灵不稳定性的困扰。这些结果表明，形式的$ξ（ϕ）r _ {\ rm gb}^2 $的GB耦合对于不含Ghost/laplacian Insmantisions的渐近Minkowski Hairy Bh Solutions的存在而起着重要作用。
In full Horndeski theories, we show that the static and spherically symmetric black hole (BH) solutions with a static scalar field~$ϕ$ whose kinetic term~$X$ is nonvanishing on the BH horizon are generically prone to ghost/Laplacian instabilities. We then search for asymptotically 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 $ϕ$ 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 $R_{\rm GB}^2$, 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 $ξ(ϕ)R_{\rm GB}^2$ plays a prominent role for the existence of asymptotically Minkowski hairy BH solutions free from ghost/Laplacian instabilities.
