Black Holes in Supergravity

黑洞被广泛认为是研究量子引力的最重要的对象。在弦理论的背景下，它们一直是研究的一个关键领域。弦理论是量子引力最有前途的方法。弦理论为黑洞的物理学提供了重要的见解。在霍金发现黑洞是热力学对象，具有关联的熵之后，利用弦理论中的技术，构造了某些类型黑洞的熵的推导。弦理论中的黑洞研究是一个非常活跃的研究领域，还有很多需要了解的地方。我建议系统地研究超引力理论中黑洞解的性质。超引力理论是爱因斯坦引力的扩展，可以用来描述弦理论的低能量极限。这些理论的超对称解具有致命的旋量。杀戮旋量的存在对解的几何形状施加了限制，例如附加的对称性，这使得它们能够被分类。超对称性在产生新的有趣的解决方案方面也特别重要，包括新的黑洞。我之前参与了许多项目，对五维超对称黑洞进行分类，并找到新的解决方案。高维黑洞之所以特别有趣，是因为最初在四维空间中形成的唯一性定理在更高维度上被分解了。例如，在五维空间中有一个黑环解决方案，它有一个环形的事件视界，与之形成对比的是五维黑洞有一个球形的事件视界。目前，关于10维和11维超引力中黑洞解的类属结构的了解相对较少，预计这些理论中将会有许多有趣的黑洞对象的例子，具有新颖的事件视界结构。为了研究这种黑洞的结构，我最近开发了新的技术。我已经成功地将它们应用于研究超对称黑洞视界附近区域的几何形状，这是一种相对简单的十维超重力理论，称为杂重超引力，并对这些解进行了完整和系统的分类。我打算扩展这一分析，并开发新的方法来分类更复杂的10维和11维超引力理论中的所有超对称黑洞解。分析将首先假设整个黑洞几何结构是超对称的，而不仅仅是地平线附近的区域。这会对几何体施加更多条件。在对这些几何形状进行分类后，我将从近视界极限外推这些解，以构建完整的黑洞解。这种分析特别适合于构建表面温度为零的黑洞。然后我将构造一个黑洞事件视界几何的分类，这些黑洞在视界附近的区域是超对称的，但在这个区域之外不是超对称的。目前已知这些解决方案的一小部分例子，系统地研究这种类型的黑洞将是很有趣的。这项研究将提供对新黑洞的几何学和物理学的见解。特别是，就像在弦理论中构建的其他类型的黑洞一样，使用弦理论技术来理解这些黑洞的熵是可能的。最近，也有人猜测，某些类型的超导体可能可以用某些类型的黑洞来描述。黑洞视界附近区域的物理性质在这种描述中起着重要作用。因此，理解超引力中的黑洞解是很有意义的。

Black holes are widely considered to be the most important objects for studying quantum gravity. In the context of string theory, which is the most promising approach to quantum gravity, they have been a key area of study. String theory has provided significant insights into the physics of black holes. Following Hawking's discovery that black holes are thermodynamical objects, which have an associated entropy, a derivation of the entropy of certain types of black holes has been constructed, using techniques in string theory. The study of black holes in string theory is a very active field of research, and there remains much to be understood. I propose to systematically investigate properties of black hole solutions of supergravity theories. Supergravity theories are extensions of Einstein's gravity, and can be used to describe the low energy limit of string theory. Supersymmetric solutions of these theories possess Killing spinors. The existence of Killing spinors imposes constraints on the geometry of the solution, such as additional symmetries, which enable them to be classified. Supersymmetry has also been particularly important in generating new and interesting solutions, including new black holes. I have previously worked on a number of projects classifying five-dimensional supersymmetric black holes, and finding new solutions. Higher dimensional black holes are particularly interesting because the uniqueness theorems, originally formulated in four dimensions, break down in higher dimensions. For example, in five dimensions there is a black ring solution, which has an annular event horizon, in contrast to the five dimensional black hole which has a spherical event horizon. At present, relatively little is known about the generic structure of black hole solutions in ten and eleven dimensional supergravity, and it is expected that there will be many examples of interesting black objects in these theories, with novel event horizon structures. I have recently developed new techniques in order to investigate the structure of such black holes. I have successfully applied these to investigate the geometry of the region near to the event horizon of supersymmetric black holes in a relatively simple type of ten-dimensional supergravity theory, called heterotic supergravity, and a complete and systematic classification of these solutions has been obtained. I intend to extend this analysis and develop new methods to classify all supersymmetric black hole solutions in more complicated ten and eleven dimensional supergravity theories. The analysis will begin with the assumption that the whole black hole geometry is supersymmetric, not only the region near to the horizon. This imposes more conditions on the geometry. Having classified these geometries, I will extrapolate the solutions away from the near-horizon limit to construct the full black hole solutions. This analysis is particularly well suited for constructing black holes with zero surface temperature. I will then construct a classification of the geometry of the event horizon of black holes which are supersymmetric in the region near to the horizon, but are not supersymmetric away from this region. A small number of examples of these solutions are currently known, and it would be interesting to systematically investigate this type of black hole. This research will provide insights into the geometry and the physics of new black holes. In particular, as has been the case with other types of black hole constructed in string theory, it may be possible to understand the entropy of these black holes using string theory techniques. Recently, it has also been conjectured that some types of superconductors may be described by certain types of black hole. The physical properties of the region near to the event horizon of the black hole play an important role in this description. It is therefore of interest to understand black hole solutions in supergravity.