  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.
