Black Holes as Effective Geometries

TL;DR

This paper reviews how classical black hole geometries emerge as effective descriptions from microstates in string theory, highlighting explicit constructions in supersymmetric cases and discussing the role of quantum effects in extending these models.

Contribution

It provides a detailed analysis of black hole microstates in string theory and demonstrates how coarse-graining leads to effective geometries, especially in supersymmetric contexts.

Findings

Explicit microstate constructions in Type II string theory on AdS_5 x S^5 and AdS_3 x S^3 x T^4.

Coarse-graining of horizon-free microstates can produce effective extremal black hole geometries.

Quantum effects may extend beyond singularities to support finite horizon areas in certain M-theory examples.

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.