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Black holes in higher dimensions

更高维度的黑洞

基本信息

批准号：
EP/H027106/1
负责人：
Pau Figueras
金额：
$ 28.64万
依托单位：
University of Cambridge
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2010
资助国家：
英国
起止时间：
2010 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FH027106%2F1
关键词：
Black holes higher dimensions

项目摘要

General relativity is our best theory to describe the gravitational force. Among one of its most striking predictions is the existence of black holes. The latter are regions of the spacetime from which nothing, even light, can escape. In four spacetime dimensions, the properties of equilibrium black holes are well-understood: they are uniquely specified by their mass and spin, they are spherically shaped, and they are dynamically stable. This last property is very important since it makes them astrophysically relevant as the endpoint of the gravitational collapse of a star. Indeed, according to our current understanding, after a sufficiently massive star has exhausted its nuclear fuel, it has no other option but to collapse and form a black hole. However, black holes contain in their interior singularities where the gravitational force becomes so extreme that general relativity breaks down. It is expected that in these situations a new theory that combines the laws of quantum mechanics with general relativity, namely a theory of quantum gravity, is required.In recent years the study of general relativity in dimensions greater than four has received a lot of attention for various reasons. First, general relativity is contained in string theory and the latter is our best candidate for a theory of quantum gravity. However, its consistency requires more than four spacetime dimensions. Second, according to recent developments, string theory (and hence gravity) in certain spacetimes is equivalent to an ordinary theory of particles, without gravity, in one spacetime dimension less. Typically, in the regime in which string theory reduces to general relativity the corresponding particle physics theory cannot be described by the standard methods in particle physics. Therefore, five-dimensional gravity, and in particular black holes, provide a novel tool to address problems in standard four-dimensional theories of particles. This new tool has proven to be very useful in a variety of contexts. For example, it has been possible to understand some properties of the quark-gluon plasma that is being produced in accelerators (e.g., the LHC). Finally, some theories predict the production of higher dimensional black holes at the LHC. The main goal of my research is to get a better understanding of higher dimensional black holes. To achieve this I propose to: study the dynamical stability of black holes, find new higher dimensional black holes and study the formation of black holes. One novel property that higher dimensional black holes have is that they can become unstable if they spin sufficiently fast. In four dimensions this cannot happen since the spin of a black hole always has an upper bound. However, the details of these instabilities are not fully understood. In my research I will study these instabilities both analytically and numerically. These instabilities typically signal the existence of new black holes. Hence, their study should give us clues about the kinds of black holes that there are and how they are related. Secondly, the general properties of higher dimensional black holes are not fully understood. In particular, it is not even known what kinds of black holes there can be. For instance, doughnut-shaped black holes have been discovered in five dimensions and they explicitly demonstrate that parameters other than the mass and the spin are needed to fully specify the black hole. In my project I will develop methods to systematically find new black holes analytically.Finally, I will use five-dimensional gravity to study the equilibration of the corresponding particle theory. This process cannot be studied analytically by standard methods, but from the gravity side it corresponds to the formation of a black hole. In addition, my results may have implications for the issue of singularity formation in general relativity, which is an interesting mathematical problem in its own right.

广义相对论是描述引力的最佳理论。其中最惊人的预言之一是黑洞的存在。后者是时空的区域，任何东西，甚至光，都无法逃脱。在四维时空中，平衡态黑洞的性质是很好理解的：它们由质量和自旋唯一指定，它们是球形的，并且它们是动态稳定的。这最后一个性质非常重要，因为它使它们在天体物理学上与星星引力坍缩的终点有关。事实上，根据我们目前的了解，足够大的星星在耗尽核燃料后，除了坍缩并形成黑洞之外别无选择。然而，黑洞在其内部包含奇点，在那里引力变得如此极端，以至于广义相对论崩溃。在这种情况下，人们期待着将量子力学和广义相对论结合起来的新理论，即量子引力理论。近年来，由于各种原因，四维以上的广义相对论的研究受到了广泛的关注。首先，广义相对论包含在弦理论中，而弦理论是量子引力理论的最佳候选者。然而，它的一致性需要超过四个时空维度。第二，根据最近的发展，弦理论（以及引力）在特定时空中等价于没有引力的、少一个时空维度的普通粒子理论，通常，在弦理论简化为广义相对论的情况下，相应的粒子物理学理论不能用粒子物理学的标准方法来描述。因此，五维引力，特别是黑洞，为解决标准四维粒子理论中的问题提供了一个新的工具。事实证明，这一新工具在各种情况下都非常有用。例如，人们已经有可能理解加速器中产生的夸克-胶子等离子体的一些性质（例如，LHC）。最后，一些理论预测了LHC中高维黑洞的产生。我研究的主要目标是更好地了解高维黑洞。为了实现这一点，我建议：研究黑洞的动力学稳定性，发现新的高维黑洞和研究黑洞的形成。高维黑洞的一个新特性是，如果它们旋转得足够快，它们会变得不稳定。在四维空间中，这是不可能发生的，因为黑洞的自旋总是有一个上限。然而，这些不稳定性的细节还没有完全了解。在我的研究中，我将从分析和数值两方面研究这些不稳定性。这些不稳定性通常表明新黑洞的存在。因此，他们的研究应该为我们提供有关黑洞种类以及它们之间关系的线索。其次，高维黑洞的一般性质还没有被完全理解。特别是，我们甚至不知道可能存在什么类型的黑洞。例如，在五维空间中已经发现了甜甜圈形状的黑洞，它们明确地表明，除了质量和自旋之外，还需要其他参数来完全指定黑洞。在我的项目中，我将开发方法来系统地发现新的黑洞分析。最后，我将使用五维引力来研究相应的粒子理论的平衡。这个过程不能用标准方法进行分析研究，但从引力的角度来看，它对应于黑洞的形成。此外，我的结果可能对广义相对论中奇点形成的问题有影响，这本身就是一个有趣的数学问题。