Abstract
A key role in black hole dynamics is played by the inner horizon; most of the entropy of a slightly nonextremal charged or rotating black hole is carried there, and the covariant entropy bound suggests that the rest lies in the region between the inner and outer horizon. An attempt to match this onto results of the microstate geometries program suggests that a `Higgs branch' of underlying long string states of the configuration space realizes the degrees of freedom on the inner horizon, while the `Coulomb branch' describes the inter-horizon region and beyond. Support for this proposal comes from an analysis of the way singularities develop in microstate geometries, and their close analogy to corresponding structures in fivebrane dynamics. These singularities signal the opening up of the long string degrees of freedom of the theory, which are partly visible from the geometry side. A conjectural picture of the black hole interior is proposed, wherein the long string degrees of freedom resolve the geometrical singularity on the inner horizon, yet are sufficiently nonlocal to communicate information to the outer horizon and beyond.
Highlights
Description obscure — how does one reconstruct the bulk geometry? Where is the black hole horizon, let alone its interior? Or for that matter any localized bulk observables? Is the gauge theory only describing the black hole exterior? Is there some complementarity map to describe the interior [2]? What about the experience of infall? There have been some attempts to construct local observables using the operator spectrum of the gauge theory, dating back to the early days of gauge/gravity duality [3, 4], but their status is unclear
A key role in black hole dynamics is played by the inner horizon; most of the entropy of a slightly nonextremal charged or rotating black hole is carried there, and the covariant entropy bound suggests that the rest ‘floats’ in the region between the inner and outer horizon
An attempt to match this onto results of the microstate geometries program suggests that a ‘Higgs branch’ of underlying long string states of the configuration space realizes the degrees of freedom on the inner horizon, while the geometrical ‘Coulomb branch’ describes the black hole exterior; the inter-horizon region has excitations from both branches
Summary
Our focus will be the set of three-charge geometries in toroidally compactified string theory. Ρ20 sinh 2α1,5,p fixed, in such a way that the D1 and D5 charges make a ‘heavy’ background geometry whose contributions to the ADM mass scale like −s 2, and the P charge is comprised of ‘light’ excitations on that background whose energies scale like 0s. This limit leads to a geometry that is locally AdS3 × S3 × T4: ds2 = √ 1 H1H5. The canonical BTZ form of the metric arrives upon making the coordinate transformation (defining the AdS radius = 4G3n1n5 in 3d Planck units, where n1,5 are the integer brane charges) r2. Rotation on the three-sphere transverse to the branes fibers the S3 over the locally AdS3 BTZ base [48]
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