Black Holes in Supergravity

超引力中的黑洞

基本信息

批准号：
ST/I004874/2
负责人：
Jan Gutowski
金额：
$ 41.56万
依托单位：
University of Surrey
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2012
资助国家：
英国
起止时间：
2012 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=ST%2FI004874%2F2
关键词：
Black Holes Supergravity

项目摘要

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.

黑洞被广泛认为是研究量子引力最重要的物体。在弦理论（最有前途的量子引力方法）的背景下，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。霍金发现黑洞是热力学物体，具有相关的熵，之后，利用弦理论技术构建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，还有很多有待理解的地方。我建议系统地研究超引力理论黑洞解的性质。超引力理论是爱因斯坦引力的延伸，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杀死旋量。杀死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。超对称性对于产生新的有趣的解决方案（包括新的黑洞）也特别重要。我之前曾参与过许多对五维超对称黑洞进行分类并寻找新解决方案的项目。高维黑洞特别有趣，因为最初在四个维度中表述的唯一性定理在更高维度中被打破。例如，在五维中存在黑环解，其具有环形事件视界，与具有球形事件视界的五维黑洞相反。目前，人们对十维和十一维超引力中黑洞解的一般结构知之甚少，预计这些理论中将会出现许多有趣的黑色物体的例子，它们具有新颖的事件视界结构。我最近开发了新技术来研究此类黑洞的结构。我成功地将这些应用于研究相对简单的十维超引力理论（称为异质超引力）中超对称黑洞事件视界附近区域的几何形状，并获得了这些解的完整系统的分类。我打算扩展这种分析并开发新的方法来对更复杂的十维和十一维超引力理论中的所有超对称黑洞解进行分类。分析首先假设整个黑洞几何形状是超对称的，而不仅仅是靠近地平线的区域。这对几何形状施加了更多条件。对这些几何形状进行分类后，我将推断出远离近地平线限制的解决方案，以构建完整的黑洞解决方案。该分析特别适合构建表面温度为零的黑洞。然后，我将构建黑洞事件视界几何形状的分类，这些黑洞在靠近视界的区域中是超对称的，但在远离该区域时不是超对称的。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会很有趣。这项研究将为新黑洞的几何结构和物理学提供见解。特别是，与弦理论中构建的其他类型黑洞的情况一样，使用弦理论技术可以理解这些黑洞的熵。最近，也有人推测某些类型的超导体可以用某些类型的黑洞来描述。黑洞事件视界附近区域的物理特性在此描述中发挥着重要作用。因此，了解超引力中的黑洞解很有意义。