Unless the reality of spacetime singularities is assumed, astrophysical black holes cannot be identical to their mathematical counterparts obtained as solutions of the Einstein field equations. Mechanisms for singularity regularization would spark deviations with respect to the predictions of general relativity, although these deviations are generally presumed to be negligible for all practical purposes. Nonetheless, the strength and nature of these deviations remain open questions, given the present uncertainties about the dynamics of quantum gravity. We present here a geometric classification of all spherically symmetric spacetimes that could result from singularity regularization, using a kinematic construction that is both exhaustive and oblivious to the dynamics of the fields involved. Due to the minimal geometric assumptions behind it, this classification encompasses virtually all modified gravity theories, and any theory of quantum gravity in which an effective description in terms of an effective metric is available. The first noteworthy conclusion of our analysis is that the number of independent classes of geometries that can be constructed is remarkably limited, with no more than a handful of qualitatively different possibilities. But our most surprising result is that this catalogue of possibilities clearly demonstrates that the degree of internal consistency and the strength of deviations with respect to general relativity are strongly, and positively, correlated. Hence, either quantum fluctuations of spacetime come to the rescue and solve these internal consistency issues, or singularity regularization will percolate to macroscopic (near-horizon) scales, radically changing our understanding of black holes and opening new opportunities to test quantum gravity.

中文翻译：

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打开黑洞核心的潘多拉魔盒

除非假设时空奇点是真实存在的，否则天体物理黑洞不能与作为爱因斯坦场方程解的数学对应物完全相同。奇点正则化机制会引发相对于广义相对论预测的偏差，尽管这些偏差通常被认为对于所有实际目的都可以忽略不计。尽管如此，鉴于目前关于量子引力动力学的不确定性，这些偏差的强度和性质仍然是悬而未决的问题。我们在这里提出了所有球对称时空的几何分类，这些分类可能由奇点正则化产生，使用的运动学结构既详尽又无视所涉及领域的动力学。由于其背后的最小几何假设，这种分类几乎涵盖了所有修正的引力理论，以及任何可以用有效度量进行有效描述的量子引力理论。我们分析的第一个值得注意的结论是，可以构建的独立几何类别的数量非常有限，只有少数几个性质不同的可能性。但我们最令人惊讶的结果是，这个可能性目录清楚地表明，相对于广义相对论，内部一致性的程度和偏差的强度是强正相关的。因此，要么时空的量子涨落来拯救并解决这些内部一致性问题，要么奇点正则化将渗透到宏观（近地平线）尺度，