在弦论中，引力熵是在微观状态的基础空间上通过粗粒化而产生的。在这篇评论中，我们想解决这样一个问题：在封闭的弦论中，经典黑洞几何本身是如何作为一个纯态的有效或近似描述而出现的，而半经典观察者无法将其与“天真”几何区分开来。在具有足够超对称性的情况下，我们可以在时空中明确地构造这些微观态，并理解非奇异、无视界物体的粗粒化如何导致作为极端黑洞的有效描述。我们讨论了这些结果是如何出现的例子在II型弦论上的AdS_5 x S^5和AdS_3 x S^3 x T^4分别保持16和8超荷。为了把黑洞作为有效几何的这种图景扩展到有限视界面积的情形，引力中量子效应的尺度必须远远超出有效理论中奇点的范围。通过研究AdS_3 x S^2 x CY上M理论中保持4个超对称的例子，我们展示了这是如何发生的。
英文摘要：
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.
All known horizonless black-hole microstate geometries correspond to brane sources that acquire a finite size, and hence break the spherical symmetry of the black hole. We construct, for the first time, solutions with zero horizon area that have the same charges as a three-charge F1-NS5-P Type-IIA black hole and preserve this spherical symmetry. The momentum of these solutions is carried by longitudinal D0-D4 density fluctuations inside the NS5-branes. We argue that these solutions should be interpreted as the long-throat limit of a family of smooth, horizonless microstate geometries, called s…
We derive a non-BPS linear ansatz using the charged Weyl formalism in string and M-theory backgrounds. Generic solutions are static and axially-symmetric with an arbitrary number of non-BPS sources corresponding to various brane, momentum and KKm charges. Regular sources are either four-charge non-extremal black holes or smooth non-BPS bubbles. We construct several families such as chains of non-extremal black holes or smooth non-BPS bubbling geometries and study their physics. The smooth horizonless geometries can have the same mass and charges as non-extremal black holes. Furthermore, we fin…
Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon. This prompts the question to what extent OTOCs display chaotic behaviour in horizonless microstate geometries. This question is complicated by the fact that Lyapunov growth of OTOCs requires nonzero temperature, whereas constructions of microstate geometries have been mostly restricted to extremal black holes. In this paper, we compute OTOCs for a class of extremal black holes, namely maximally rotating BTZ black holes, and show that on averag…
Thermal Decay without Information Loss in Horizonless Microstate Geometries
我们开发了一种新的混合WKB技术来计算边界到边界的标量格林函数在渐近AdS背景中的标量波动方程是可分离的，是明确的渐近区域可解。我们将这种技术应用到一族六维$\frac{1}{8}$ -BPS渐近AdS $_3\,\times\,$ S $^3$的无视界几何中，这些几何具有与具有大视界面积的D1-D5-P黑洞相同的电荷和角动量。在大的和中等的距离，这些几何非常接近极端BTZ $\,\times\,$ S $^3$几何的黑洞，但不是有一个事件视界，这些几何有一个光滑的高度红移的全球AdS $_3\,\times\,$ S $^3$帽在IR。我们表明，响应函数的标量探测器，在动量空间，基本上由BTZ响应函数调制的高度红移的全局AdS $_3$的极点结构给出。在位置空间中，这转化为一个尖锐的指数黑洞般的衰变，时间短于$N_1 N_5$，随后出现均匀间隔的“来自帽盖的回声”，周期为$\sim N_1 N_5$。我们的结果表明，无水平微观态几何可以有相同的热衰减的黑洞没有相关的信息损失。
Microstate geometries in string theory replace the black-hole horizon with a smooth geometric "cap" at the horizon scale. In geometries constructed using superstratum technology, this cap has the somewhat surprising property that induces very large tidal deformations on infalling observers that are far away from it. We find that this large-distance amplification of the tidal effects is also present in horizonless microstate geometries constructed as bubbling solutions, but can be tamed by suitably arranging the bubbles to reduce the strength of some of the gravitational multipole moments. Howe…
Black hole entropy is a robust prediction of quantum gravity with no established phenomenological consequences to date. We use the Bekenstein-Hawking entropy formula and general-relativistic statistical mechanics to determine the probability distribution of random geometries uniformly sampled in phase space. We show that this statistics (in the limit $\hbar\to 0$) is relevant to large curvature perturbations, resulting in a population of primordial black holes with zero natal spin. In principle, the identification of such a population at LIGO, Virgo, and future gravitational wave observatories…
We present a slowly rotating generalization of a black hole modeled by a Solv horizon geometry, in five dimensional General Relativity. A separable ansatz compatible with Einstein equations is proposed, which is integrated in terms of hypergeometric and exponential functions. The solution highly simplifies after requiring to maintain the same asymptotic behaviour as the non-rotating black hole and to have finite, non-vanishing charges. We compute the charges of the solution and also comment on its importance for studying the phase space of the theory in this sector.
We construct a family of non-supersymmetric extremal black holes and their horizonless microstate geometries in four dimensions. The black holes can have finite angular momentum and an arbitrary charge-to-mass ratio, unlike their supersymmetric cousins. These features make them and their microstate geometries astrophysically relevant. Thus, they provide interesting prototypes to study deviations from Kerr solutions caused by new horizon-scale physics. In this paper, we compute the gravitational multipole structure of these solutions and compare them to Kerr black holes. The multipoles of the b…
Gravitational solutions involving shockwaves have attracted significant recent interest in the context of black holes and quantum chaos. Certain classes of supersymmetric two-charge black hole microstates are described by supergravity solutions containing shockwaves, that are horizonless and smooth away from the shockwave. These configurations have been used to describe how black hole microstates absorb and scramble perturbations. In this paper we construct the first family of asymptotically flat supersymmetric three-charge microstate solutions that contain shockwaves. We identify a family of …
We argue that the fundamental "atomic objects" in string theory are themelia: extended objects that have 16 supersymmetries locally. We show that all existing smooth horizonless microstate geometries can be seen as bound states of themelia, and we conjecture that all such bound states with suitable KKM charges will give rise to microstate geometries. We also construct the most general themelion with a three-torus isometry and show that it interpolates between superstrata and the super-maze.
We prove existence of all possible bi-axisymmetric near-horizon geometries of 5-dimensional minimal supergravity. These solutions possess the cross-sectional horizon topology $S^3$, $S^1\times S^2$, or $L(p,q)$ and come with prescribed electric charge, two angular momenta, and a dipole charge (in the ring case). Moreover, we establish uniqueness of these solutions up to an isometry of the symmetric space $G_{2(2)}/SO(4)$.
