Black Holes in Supergravity

黑洞被广泛认为是研究量子引力最重要的对象。在弦理论的背景下，这是量子引力最有前途的方法，它们一直是研究的关键领域。弦理论为黑洞物理学提供了重要的见解。在霍金发现黑洞是具有相关熵的天体之后，人们利用弦理论中的技巧推导出了某些类型黑洞的熵。在弦理论中对黑洞的研究是一个非常活跃的研究领域，还有很多东西有待理解。我建议系统地研究超引力理论的黑洞解的性质。超引力理论是爱因斯坦引力理论的延伸，可以用来描述弦理论的低能极限。这些理论的超对称解具有Killing旋量。Killing旋量的存在对解的几何形状施加了限制，例如额外的对称性，这使得它们能够被分类。超对称性在产生新的和有趣的解决方案方面也特别重要，包括新的黑洞。我以前曾参与过一些项目，对五维超对称黑洞进行分类，并找到新的解决方案。高维黑洞特别有趣，因为最初在四维中表述的唯一性定理在高维中失效了。例如，在五维空间中，有一个黑环解，它有一个环形的事件视界，与五维黑洞相反，它有一个球形事件视界。目前，人们对10维和11维超引力中黑洞解的一般结构知之甚少，预计在这些理论中会有许多有趣的黑色物体的例子，具有新颖的事件视界结构。我最近开发了新的技术来研究这种黑洞的结构。我已经成功地应用这些调查的几何形状的区域附近的事件视界的超对称黑洞在一个相对简单的类型的10维超引力理论，所谓的杂化超引力，和一个完整的和系统的分类，这些解决方案已经获得。我打算扩展这种分析，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。分析开始时假设整个黑洞的几何形状是超对称的，而不仅仅是视界附近的区域。这对几何体施加了更多的条件。在对这些几何进行分类之后，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造表面温度为零的黑洞。然后，我将构建一个分类的黑洞的事件视界的几何形状是超对称的在该地区的视界附近，但不是超对称远离这个地区。目前已知这些解决方案的少数例子，系统地研究这种类型的黑洞将是有趣的。这项研究将为新黑洞的几何和物理学提供见解。特别是，就像在弦论中构造的其他类型的黑洞一样，用弦论技术来理解这些黑洞的熵是可能的。最近，也有人提出，某些类型的超导体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一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.