Holomorphic waves of black hole microstructure

Abstract

We obtain the largest families constructed to date of 1 8 -BPS solutions of type IIB supergravity. They have the same charges and mass as supersymmetric D1-D5-P black holes, but they cap off smoothly with no horizon. Their construction relies on the structure of superstratum states, but allows the momentum wave to have an arbitrary shape. Each family is based on an arbitrary holomorphic function of one variable. More broadly, we show that the most general solution is described by two arbitrary holomorphic functions of three variables. After exhibiting several new families of such "holomorphic superstrata," we reformulate the BPS backgrounds and equations in holomorphic form and show how this simplifies their structure. The holomorphic formulation is thus both a fundamental part of superstrata as well as an effective tool for their construction. In addition, we demonstrate that holomorphy provides a powerful tool in establishing the smoothness of our solutions without constraining the underlying functions. We also exhibit new families of solutions in which the momentum waves of the superstrata are highly localized at infinity but diffuse and spread into the infra-red limit in the core of the superstratum. Our work also leads to some results that can be tested within the dual CFT.

Microstate geometries from gauged supergravity in three dimensions

“…Here we will be concerned with S 3 compactifications of six-dimensional supergravity coupled to some tensor multiplets, and the corresponding three-dimensional gauged supergravity theory. We will also show the consistent truncation encodes some rich families of superstrata, some of which have been constructed elsewhere [7,17].…”

“…The construction of BPS/supersymmetric microstate geometries in five and six dimensions is now a well-developed art [2][3][4][5][6][7][8]. In particular, superstrata represent one of the broadest families of such geometries and have the advantage of a highly developed holographic dictionary [4][5][6][9][10][11][12][13][14][15].…”

“…One of the remarkable features that has become evident in recent constructions of asymptotically-AdS superstrata [5,7,17] is that most of the interesting physics of superstrata is encoded in a three-dimensional space-time, K. Indeed, the six-dimensional space-time of a superstratum naturally decomposes into the S 3 surface around the branes, the radial coordinate, r, and the common directions, (t, y) along the branes. 1 The manifold, K, is the geometry described by the coordinates (t, y, r) that are complementary to the S 3 .…”

Counting superstrata

“…The high-frequency mode can generally be coiffured away [47], as long as the supercharged modes are turned on. On the other hand, how to coiffure the low-frequency mode is known only on a case-by-case basis; see [29,91] for explicitly worked out examples.…”

“…As mentioned in 4.3.7, it is not yet known how to construct general multi-mode superstrata including all (k, m, n, f ). In [91], interesting progress was made by considering holomorphic superposition of some family of modes. For example, in section 4.3.5, we discussed (1, 0, n) Here, we defined…”