arXiv 2502.044302025-02astro-ph.COgr-qchep-phhep-th

标准模型及超出标准模型情形下原初黑洞的Page时间

Page Time of Primordial Black Holes in the Standard Model and Beyond

Yuber F. Perez-Gonzalez

备注：: 12 pages, 6 figures. Added references and improved figures. Matches version accepted for publication in PRD. v3: Added values for spin 3/2 particles

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AI总结：

本研究探究标准模型及超出标准模型下原初黑洞的Page时间特性，分析其对粒子组分、黑洞质量与角动量的依赖，给出相关定量结果并讨论对原初黑洞现象学的意义。

摘要：

Page时间标志着发射出的霍金辐射的冯·诺依曼熵等于正在蒸发的黑洞的贝肯斯坦-霍金熵的时刻，后者被认为可量化从外部观测到的黑洞自由度。超过这一时刻后，基于幺正性，我们预期辐射的熵会开始下降，确保信息最终能被恢复。在本研究中，我们探究了Page时间对黑洞性质以及自然界粒子组分的依赖关系。具体而言，我们分析了它对标准模型（Standard Model, SM）以及潜在的超出标准模型（Beyond-the-SM）自由度的敏感性，同时纳入了粒子质量的影响。我们发现，假设仅发射SM粒子，初始质量为$6.23\times 10^{14}~{\rm g}$的史瓦西原初黑洞（primordial black hole, PBH）的Page时间等于宇宙年龄。我们进一步探究了不可忽略的PBH角动量的影响，发现轻自旋2粒子主要在Page时间之前被发射。具体来说，对于初始质量$M_{\rm BH} \lesssim 10^{10}~{\rm g}$的PBH，当初始角动量值超过$a_\star > 0.5$时，约70%的总引力子发射发生在Page时间之前。最后，我们讨论了这一结果对PBH现象学的意义，特别是关于$ΔN_{\rm eff}$测量可能带来的约束。

英文摘要：

The Page time marks the moment when the von Neumann entropy of the emitted Hawking radiation equals the Bekenstein-Hawking entropy of an evaporating black hole, which is assumed to quantify its degrees of freedom as seen from the outside. Beyond this point, from unitarity we would expect that the entropy of the radiation begins to decrease, ensuring that information is eventually recovered. In this work, we investigate the dependence of the Page time on black hole properties and the particle content of nature. Specifically, we analyze its sensitivity to the Standard Model (SM) and potential Beyond-the-SM degrees of freedom, incorporating the effects of particle masses. We find that a Schwarzschild primordial black hole (PBH) with an initial mass of $6.23\times 10^{14}~{\rm g}$ would have a Page time equal to the age of the Universe, assuming emission of SM particles only. We further explore the impact of a non-negligible PBH angular momentum, finding that light spin-2 particles are predominantly emitted before the Page time. Specifically, for initial angular momenta values exceeding $a_\star > 0.5$, approximately $70\%$ of the total graviton emission occurs prior to the Page time for PBHs with an initial mass $M_{\rm BH} \lesssim 10^{10}~{\rm g}$. Finally, we discuss the implications for PBH phenomenology, particularly regarding potential constraints from $ΔN_{\rm eff}$ measurements.

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