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arXiv 1909.04057gr-qcastro-ph.HEhep-th
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快速旋转Kerr黑洞的量子发射谱：离散还是连续？

The quantum emission spectra of rapidly-rotating Kerr black holes: discrete or continuous?

Shahar Hod

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6 pages
发表信息：
Physics Letters B 749, 115 (2015)
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摘要：

贝肯斯坦和穆哈诺夫（BM）提出，在量子引力理论中，黑洞可能有离散的发射光谱。利用时间-能量不确定原理他们还表明，对于（非旋转）史瓦西黑洞，黑洞发射线的自然加宽$δω$在谱线的特征频率间隔$Δω$：$ζ^{\text{Sch}}\equivδω/Δω\ll1$所设定的尺度上是很小的。因此，BM得出结论，量子化史瓦西黑洞的预期离散发射线不太可能重叠。本文计算了快速旋转Kerr黑洞BM发射谱的特征无量纲比$ζ(\bar a)\equivδω/Δω$（这里$\bar a\equiv J/M^2$是黑洞的无量纲角动量）.结果表明，$ζ(\bar a)$是黑洞角动量的增函数。特别是，我们发现，克尔黑洞的量子发射线的制度$\bar a\gtrsim 0.9$的特点是无量纲比$ζ(\bar a)\gtrsim1$，因此有效地混合在一起。因此，我们的研究结果表明，即使这些快速旋转的克尔黑洞的基本质量（能量）谱是基本上离散的建议由贝肯斯坦和Mukhanov，自然加宽现象（与时间-能量不确定原理）预计将涂抹黑洞辐射谱成一个连续。

英文摘要：

Bekenstein and Mukhanov (BM) have suggested that, in a quantum theory of gravity, black holes may have discrete emission spectra. Using the time-energy uncertainty principle they have also shown that, for a (non-rotating) Schwarzschild black hole, the natural broadening $δω$ of the black-hole emission lines is expected to be small on the scale set by the characteristic frequency spacing $Δω$ of the spectral lines: $ζ^{\text{Sch}}\equivδω/Δω\ll1$. BM have therefore concluded that the expected discrete emission lines of the quantized Schwarzschild black hole are unlikely to overlap. In this paper we calculate the characteristic dimensionless ratio $ζ(\bar a)\equivδω/Δω$ for the predicted BM emission spectra of rapidly-rotating Kerr black holes (here $\bar a\equiv J/M^2$ is the dimensionless angular momentum of the black hole). It is shown that $ζ(\bar a)$ is an increasing function of the black-hole angular momentum. In particular, we find that the quantum emission lines of Kerr black holes in the regime $\bar a\gtrsim 0.9$ are characterized by the dimensionless ratio $ζ(\bar a)\gtrsim1$ and are therefore effectively blended together. Our results thus suggest that, even if the underlying mass (energy) spectrum of these rapidly-rotating Kerr black holes is fundamentally discrete as suggested by Bekenstein and Mukhanov, the natural broadening phenomenon (associated with the time-energy uncertainty principle) is expected to smear the black-hole radiation spectrum into a continuum.

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