It has been recently proposed that Hawking evaporation might slow down after a black hole has lost about half of its mass. Such an effect, called “memory burden”, is parameterized as a suppression in the mass loss rate by negative powers n of the black hole entropy and could considerably extend the lifetime of a black hole. We study the impact of memory burden on the Primordial Black Hole (PBH) reheating scenario. Modified PBH evaporation leads to a significantly longer PBH dominated stage. Requiring that PBHs evaporate prior enough to Big Bang Nucleosynthesis shrinks the allowed PBH mass range. Indeed, we find that for n > 2.5 the PBH reheating scenario is not viable. The frequency of the Gravitational Waves (GWs) induced by PBH number density fluctuations is bound to be larger than about a Hz, while the amplitude of the GW spectrum is enhanced due to the longer PBH dominated phase. Interestingly, we show that, in some models, the slope of the induced GW spectrum might be sensitive to the modifications to Hawking evaporation, proving it may be possible to test the “memory burden” effect via induced GWs. Lastly, we argue that our results could also apply to general modifications of Hawking evaporation.

中文翻译：

---

用来自原始黑洞主导宇宙的引力波探测改进的霍金蒸发


最近有人提出，霍金蒸发可能会在黑洞失去大约一半的质量后减慢。这种效应被称为“内存负担”，被参数化为黑洞熵的负幂 n 对质量损失率的抑制，并且可以大大延长黑洞的寿命。我们研究了记忆负担对原始黑洞 （PBH） 再加热情景的影响。改良的 PBH 蒸发导致 PBH 占主导地位的阶段明显更长。要求 PBH 在大爆炸核合成之前蒸发，会缩小允许的 PBH 质量范围。事实上，我们发现对于 n > 2.5 PBH 再加热方案是不可行的。由 PBH 数密度波动引起的引力波 （GW） 的频率必然大于约 1 Hz，而由于 PBH 占主导地位的相位较长，GW 谱的振幅会增强。有趣的是，我们表明，在某些模型中，诱导 GW 光谱的斜率可能对霍金蒸发的修改很敏感，证明可以通过诱导 GW 来测试“记忆负担”效应。最后，我们认为我们的结果也适用于霍金蒸发的一般修改。