标题： Kerr黑洞的自发非线性标量化 显示英文标题

标题： Spontaneous nonlinear scalarization of Kerr black holes

摘要： 正如过去几年广为人知的那样，爱因斯坦-标量-高斯-博内特（EsGB）理论避开了无毛定理，并允许标量化的致密天体包括黑洞（BH）。定义该理论的耦合函数在标量化的过程和性质中起着主要作用。选择合适的耦合函数，该理论在某种意义上是广义相对论（GR）的扩展，即任何满足GR场方程的解在EsGB理论中仍然是解，但如果时空曲率超过某个阈值，它可能会变得不稳定。因此，黑洞可以自发地标量化。对此现象最广泛研究的驱动机制是由于标量场的有效负平方质量引起的泰奇onic不稳定性。然而，即使选择耦合使得该质量为零，相对于标量场的高阶项可能导致所谓的非线性标量化。在本文中，我们通过求解非线性克莱因-戈登方程，在固定背景下演化标量场，研究Kerr黑洞如何自发地标量化。我们考虑了两种带有高阶项的不同耦合函数，一种产生非零的有效质量，另一种则不产生。我们在Kerr参数空间中对其质量和自旋进行扫描，并在场达到平衡静态状态时通过最终的演化得到标量电荷。当不存在泰奇onic不稳定性时，不存在探测极限使得黑洞以零电荷标量化，即光秃黑洞和带毛黑洞之间存在一个间隙，它们只有在质量与电荷同时趋于零时才会连接。 显示英文摘要

摘要： As it became well known in the past years, Einstein-scalar-Gauss-Bonnet (EsGB) theories evade no-hair theorems and allow for scalarized compact objects including black holes (BH). The coupling function that defines the theory is the main character in the process and nature of scalarization. With the right choice, the theory becomes an extension of general relativity (GR) in the sense any solution to the GR field equations remains a solution in the EsGB theory, but it can destabilize if a certain threshold value of the spacetime curvature is exceeded. Thus BHs can spontaneously scalarized. The most studied driving mechanism to this phenomenon is a tachyonic instability due to an effective negative squared mass for the scalar field. However, even when the coupling is chosen such that this mass is zero, higher order terms with respect to the scalar field can lead to what is coined nonlinear scalarization. In this paper we investigate how Kerr BHs spontaneously scalarize by evolving the scalar field on a fixed background via solving the nonlinear Klein-Gordon equation. We consider two different coupling functions with higher order terms, one that yields a non-zero effective mass and another that does not. We sweep through the Kerr parameter space in its mass and spin and obtain the scalar charge by the end of the evolution when the field settles in an equilibrium stationary state. When there is no tachyonic instability present, there is no probe limit in which the BH scalarizes with zero charge, i.e. there is a gap between bald and hairy BHs and they only connect when the mass goes to zero together with the charge.