近日，韩国基础科学研究所(IBS)宇宙理论物理中心的Miok Park及其研究团队取得一项新进展。经过不懈努力，他们对EsGB理论中毛状黑洞的标量场扰动进行研究。相关研究成果已于2024年8月21日在国际知名学术期刊《高能物理杂志》上发表。

该研究团队研究了在爱因斯坦-标量-高斯-邦纳理论中，涉及全局U(1)对称性自发破缺的毛状黑洞的标量场扰动，这一研究适用于渐近平直时空。研究人员探究了无毛黑洞在耦合常数的临界点变得不稳定，并通过自发对称性破缺驱动，经历相变转变为对称性破缺相中的毛状黑洞的机制。由于高斯-邦纳项在无穷远处的影响逐渐减弱，这种转变发生在黑洞视界附近。

为了研究这一过程，研究人员在新形成的背景时空上引入了一个标量场扰动，并使用格林函数方法求解了线性化扰动方程。研究人员首先求解了格林函数，并考虑了分支割线的贡献，这使他们能够分析扰动在空间和零无穷远处的晚期行为。研究人员发现，晚期行为仅通过一个质量项与史瓦西黑洞不同。随后，研究人员继续数值计算了由格林函数中的极点引起的准正态模（QNMs）。

该研究的主要兴趣在于利用QNMs来研究对称相和对称性破缺相中黑洞解的稳定性。与之前的研究一致，这项分析表明，当二次耦合常数超过四次耦合常数固定值的临界值时，对称相中的毛状黑洞会变得不稳定。相比之下，对称性破缺相中的毛状黑洞在临界值处总是稳定的。这些数值结果提供了强有力的证据，表明了一个动力学过程：无毛的不稳定黑洞通过自发对称性破缺转变为对称性破缺相中的稳定毛状黑洞。

附：英文原文

Title: Scalar field perturbation of hairy black holes in EsGB theory

Author: Hyun, Young-Hwan, Latosh, Boris, Park, Miok

Issue&Volume: 2024-08-21

Abstract: We investigate scalar field perturbations of the hairy black holes involved with spontaneous symmetry breaking of the global U(1) symmetry in Einstein-scalar-Gauss-Bonnet theory for asymptotically flat spacetimes. We consider the mechanism that black holes without hairs become unstable at the critical point of the coupling constant and undergo a phase transition to hairy black holes in the symmetry-broken phase driven by spontaneous symmetry breaking. This transition occurs near the black hole horizon due to the diminishing influence of the Gauss-Bonnet term at infinity. To examine such process, we introduce a scalar field perturbation on the newly formed background spacetime. We solve the linearized perturbation equation using Green’s function method. We begin by solving the Green’s function, incorporating the branch cut contribution. This allows us to analytically investigate the late-time behavior of the perturbation at both spatial and null infinity. We found that the late-time behavior only differs from the Schwarzschild black hole by a mass term. We then proceed to calculate the quasinormal modes (QNMs) numerically, which arise from the presence of poles in the Green’s function. Our primary interest lies in utilizing QNMs to investigate the stability of the black hole solutions both the symmetric and symmetry-broken phases. Consistent with the prior study, our analysis shows that hairy black holes in the symmetric phase become unstable when the quadratic coupling constant exceeds a critical value for a fixed value of the quartic coupling constant. In contrast, hairy black holes in the symmetry-broken phase are always stable at the critical value. These numerical results provide strong evidence for a dynamical process that unstable black holes without hairs transition into stable hairy black holes in the symmetry-broken phase through the spontaneous symmetry breaking.

DOI: 10.1007/JHEP08(2024)163

Source: https://link.springer.com/article/10.1007/JHEP08(2024)163