In general relativity, astrophysical black holes (BHs) are simple objects, described by just their mass and spin. These simple solutions are not exclusive to general relativity, as they also appear in theories that allow for an extra scalar degree of freedom. Recently, it was shown that some theories which couple a scalar field with the Gauss–Bonnet invariant can have the same classic black hole solutions from general relativity as well as hairy BHs. These scalarized solutions can be stable, having an additional “charge” term that has an impact on the gravitational-wave emission by black hole binaries. In this paper, we overview black hole solutions in scalar-Gauss–Bonnet gravity, considering self-interacting terms for the scalar field. We present the mode analysis for the monopolar and dipolar perturbations around the Schwarzschild black hole in scalar-Gauss–Bonnet, showing the transition between stable and unstable solutions. We also present the time-evolution of scalar Gaussian wave packets, analyzing the impact of the scalar-Gauss–Bonnet term in their evolution. We then present some scalarized solutions, showing that nonlinear coupling functions and self-interacting terms can stabilize them. Finally, we compute the light-ring frequency and the Lyapunov exponent, which possibly estimate the black hole quasinormal modes in the eikonal limit.

中文翻译：

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标量-高斯-博内引力中黑洞的标量模式、自发标量化和圆形零测地线

在广义相对论中，天体物理黑洞 (BH) 是简单的物体，仅通过它们的质量和自旋来描述。这些简单的解决方案并不是广义相对论独有的，因为它们也出现在允许额外标量自由度的理论中。最近，研究表明，一些将标量场与 Gauss-Bonnet 不变量耦合的理论可以具有来自广义相对论的经典黑洞解以及多毛 BH。这些标量化解可以是稳定的，具有额外的“电荷”项，对黑洞双星的引力波发射有影响。在本文中，我们概述了标量-高斯-博内引力中的黑洞解决方案，考虑了标量场的自交互项。我们提出了标量-高斯-博内特中史瓦西黑洞周围单极和偶极扰动的模式分析，显示了稳定解和不稳定解之间的过渡。我们还展示了标量高斯波包的时间演化，分析了标量-高斯-博内项在其演化中的影响。然后，我们提出了一些标量化解决方案，表明非线性耦合函数和自交互项可以稳定它们。最后，我们计算了光环频率和李雅普诺夫指数，这可能估计黑洞准正态模式在 eikonal 极限。然后，我们提出了一些标量化解决方案，表明非线性耦合函数和自交互项可以稳定它们。最后，我们计算了光环频率和李雅普诺夫指数，这可能估计黑洞准正态模式在 eikonal 极限。然后，我们提出了一些标量化解决方案，表明非线性耦合函数和自交互项可以稳定它们。最后，我们计算了光环频率和李雅普诺夫指数，这可能估计黑洞准正态模式在 eikonal 极限。