Black holes in higher dimensions, black strings, and the Gregory-Laflamme instability

黑洞是爱因斯坦广义相对论的一个重要预言。今天，有强有力的观测证据表明天体物理学黑洞的存在。另一方面，作为量子引力理论和所有相互作用统一理论的主要候选理论，弦理论在其低能量极限下预测了额外的场，并且还需要更高的维度来保持数学一致性。因此，黑洞的基本属性会发生巨大的变化。在这个项目中，我们想要研究高维黑洞的性质，并研究它们如何受到额外维度紧化的影响。特别是，我们打算研究黑洞和黑弦，即具有不同类型视界拓扑的黑色物体，存在于具有或不具有紧维的高维时空中。我们打算解决拓扑变化转换的重要问题，例如当黑弦演变成黑洞时。我们将着重讨论这些黑色物体的稳定性问题。特别是，我们将讨论与黑色物体新分支的出现有关的格雷戈里-拉弗拉姆不稳定性。我们还打算揭示这些黑色物体的热力学稳定性和经典引力稳定性的关系。最后，针对膜世界模型中的黑洞，我们打算对实验室实验中额外维度的可观测性问题做出重大贡献。

Black Holes are a major prediction of Einstein's general relativity. Today there is strong observational evidence for the existence of astrophysical black holes. On the other hand string theory, a major candidate for the quantum theory of gravity and the unification of all interactions, predicts in its low energy limit additional fields and also requires higher dimensions for mathematical consistency. As a result, essential properties of black holes can change dramatically. In this project we want to investigate the properties of black holes in higher dimensions and study how they are affected by the compactification of extra dimensions. In particular, we intend to investigate black holes and black strings, i.e. black objects with different types of horizon topologies, present in higher dimensional spacetimes with or without compact dimensions. We intend to resolve the important issue of topology changing transitions, when e.g. black strings evolve into black holes. We will put emphasis on the question of stability of these black objects. In particular, we will address the Gregory-Laflamme instability, associated with the emergence of new branches of black objects. We also intend to enlighten the relation of thermodynamic stability and classical gravitational stability of these black objects. Addressing finally black holes in braneworld models, we intend to contribute significantly to questions of observability of extra dimensions in lab experiments.