Black Holes as Effective Geometries

TL;DR

This work argues that classical black hole geometries can emerge as effective, coarse-grained descriptions of complex horizon-free microstates in string theory, particularly in highly supersymmetric settings. It develops a framework where smooth supergravity solutions form a phase-space that, upon quantization, yields a microstate Hilbert space whose typical states are indistinguishable by semiclassical probes, producing black-hole–like entropies via coarse graining. Across AdS5×S5, AdS3×S3×T4, and AdS3×S2 backgrounds, the authors demonstrate explicit mappings between CFT ensembles and bulk geometries (e.g., LLM droplets, D1-D5 microstates, and multicenter BPS solutions), showing that finite-horizon black holes can arise as effective descriptions of complicated horizon-free configurations, with quantum fluctuations extending beyond naive singular regions. They also emphasize the role of phase-space quantization, coherence, and the no-hair-like features of typical ensembles, while discussing conditions under which scaling solutions and large-scale quantum effects modify or cap the emergent throats, thereby shaping the bulk interpretation of black hole entropy and information retention.

Abstract

Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or approximate description of a pure state, in a closed string theory, which semiclassical observers are unable to distinguish from the "naive" geometry. In cases with enough supersymmetry it has been possible to explicitly construct these microstates in spacetime, and understand how coarse-graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise for examples in Type II string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8 supercharges respectively. For such a picture of black holes as effective geometries to extend to cases with finite horizon area the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective theory. By studying examples in M-theory on AdS_3 x S^2 x CY that preserve 4 supersymmetries we show how this can happen.

Figures (2)

• Figure 1: Relationship between various components appearing in the study of black hole microstates and black holes as effective geometries. The smooth geometries making up the phase space can be thought of either as classical solutions defining a solution space (isomorphic to a phase space) or as highly-localized phase space densities corresponding to coherent states. The black hole at the bottom of the figure is then to be generated by coarse graining (in some suitable sense) over a large number of underlying horizon-free configurations; the resultant geometry need not be a black hole but may, for instance, include a naked singularity. The details can differ significantly between examples -- the quantization, for instance, is rather different for the 1/4 and 1/8 BPS case. The "thermal states" in the BPS sector box refer to ensembles with any chemical potential that couples to an operator that commutes with supersymmetry, and thus acts within the BPS Hilbert space (for example the left-moving temperature in a 2d CFT while the right-movers are kept in their ground state).
• Figure 2: Sketch of a 3-center attractor flow tree from Denef:2007vgdeBoer:2008fk. The dark blue lines are lines of marginal stability, the purple lines are single center attractor flows. The tree starts at the yellow circle (the moduli at infinity) and flows towards the attractor points indicated by the yellow boxes. Note here that $\Gamma_4 = \Gamma_1 + \Gamma_2$ and $\Gamma = \Gamma_4 + \Gamma_3$. On the walls of marginal stability the moduli are such that $|Z(\Gamma; t)| = |Z(\Gamma_3;t)| + |Z(\Gamma_4; t)|$ (horizontal wall on top) and $|Z(\Gamma_4; t)| = |Z(\Gamma_1; t)| + |Z(\Gamma_2;t)|$ (diagonal wall on bottom left).