Black holes as effective geometries

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 ×S 5 and on AdS 3 ×S 3 ×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 ×S 2 ×CY that preserve 4 supersymmetries we show how this can happen. This review is a revised and extended version of proceedings submitted for the Sower's Theoretical Physics Workshop 2007 "What is String Theory?" and of lecture notes for the CERN RTN Winter School on Strings, Supergravity and Gauge Theories [1].

The black hole S-Matrix from quantum mechanics

“…While the fuzzball program [12][13][14][15][16] provides some arguments for why stringy details may be important, it is fair to say that there is no general consensus on the matter.…”

Non-BPS multi-bubble microstate geometries

“…The most successful approach to constructing such structure, passing all of the above tests, is the fuzzball programme in string theory [19][20][21][22][23][24]. In this programme one often considers semi-classical microstates, which are well-described within supergravity.…”

Foliation-dependence of CFTs in Lorentzian-AdS/CFT

“…The coordinate transformations (48) and (49) are analogous to the coordinate transformation to go from Minkowski spacetime to Rindler spacetime [31] and so, even though the CFT in the diamond is the same as the global-CFT, we refer to it as Rindlerized-global-CFT as it is restricted to the causal diamond.…”

“…10 We thank Masaki Shigemori for discussions on this point. 11 For a review on fuzzballs see [45][46][47][48][49][50]. 12 For an alternate proposal for modifying the bulk see [22].…”