通过自发对称性破缺的带毛黑洞的宇宙学意义：带毛黑洞是原初的吗？
Cosmological implications for hairy black holes via spontaneous symmetry breaking: Are Hairy Black Holes Primordial?
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- Institute for Basic Science (IBS)（韩国基础科学研究院）
- University of Warsaw（华沙大学）
- Pusan National University（釜山国立大学）
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中文总结 AI 辅助
本研究探讨ESGB理论中自发对称破缺产生的带毛黑洞是否与宇宙演化兼容，推导了耦合强度等的严格约束，发现仅质量约几克的超轻黑洞可形成标量毛，即带毛原初黑洞。
中文摘要 AI 辅助
我们研究在爱因斯坦-标量-高斯-邦内（ESGB）理论中，由自发对称性破缺产生的带毛黑洞（该理论包含具有整体U(1)对称性的复标量场）是否能与宇宙演化兼容。为此，我们引入ESGB理论，其中标量自相互作用在宇宙学尺度上起作用，而在黑洞附近可忽略。由于GB项在宇宙学尺度上的时间依赖性，演化的FLRW背景中标量场的动力学与近静态黑洞背景中的动力学存在质的差异。特别是，对于与带毛黑洞形成兼容的标量-GB耦合，有效势在整个暴胀期间都支持对称性破缺的真空。然而，暴胀之后，减速膨胀会改变GB项的符号，使有效势暂时变得无下界。随着GB贡献随后减小，标量自相互作用最终占主导并恢复对称性。在该示意图框架内，我们对耦合强度、截断尺度和黑洞质量推导了严格约束，这些约束主要源于避免在无下界阶段标量场扰动的快子放大。对于与宇宙演化和标量毛形成都兼容的截断尺度，我们发现只有质量约为几克的超轻黑洞才能形成标量毛，从而将其识别为带毛原初黑洞。
英文摘要
We investigate whether hairy black holes generated through spontaneous symmetry breaking in Einstein-Scalar-Gauss-Bonnet (ESGB) theory, involving a complex scalar field with a global $U(1)$ symmetry, can be compatible with cosmological evolution. To this end, we introduce the ESGB theory with a scalar self-interaction that becomes relevant on cosmological scales while remaining negligible near the black hole. Owing to the time dependence of the GB term on cosmological scales, the scalar field dynamics in the evolving FLRW background differ qualitatively from those in the nearly static black hole background. In particular, for scalar-GB couplings compatible with hairy black hole formation, the effective potential supports a symmetry-broken vacuum throughout inflation. However, after inflation, a decelerated expansion changes the sign of the GB term, temporarily making the effective potential unbounded from below. As the GB contribution subsequently decreases, the scalar self-interaction eventually dominates and restores the symmetry. Within this schematic framework, we derive stringent constraints on the coupling strengths, the cutoff scale, and the black hole mass, which primarily arise for avoiding efficient tachyonic amplification of the scalar field perturbations during the unbounded phase. For cutoff scales compatible with both cosmological evolution and scalar hair formation, we find that only ultralight black holes with masses of the order of a few grams can develop scalar hair, identifying them as hairy primordial black holes.
