Black Rings, Vortons and Saturns: a `Dictionary´

许多场论模型具有沿某一方向无限延伸和单位长度有限质量的类弦解。在一个简单的启发式构造中，人们可以通过取一个这样的物体的有限块并将其两端连接起来形成一个环来获得新的构型。然后，通过离心力稳定回路，防止收缩，从而产生具有固有环形拓扑结构的平衡结构。这种解的例子是高维广义相对论中的黑环和在四维平坦时空中表述的一些经典场论模型中的涡。在这个项目中，我们打算研究黑环和涡旋之间的类比，超越这个简单的启发式结构。这将产生一个黑环-涡顿“字典”，从而更好地理解这两种类型的配置，并发现新的解决方案。特别是，这个类比表明，我们打算找到描述“土星”和“双涡子”的复合多孤子的存在。我们还计划研究离心力是否可以被电磁相互作用取代以达到平衡。通过构造具有宇宙学常数的黑环和涡，我们将回答时空的非渐近平坦结构如何影响环拓扑解的问题。

A number of field theory models possess string-like solutions with infinite extent along some direction and finite mass per unit length. In a simple heuristic construction, one can obtain new configurations by taking a finite piece of such an object and joining the ends to form a loop. The loop is then stabilized against contraction by a centrifugal force, thereby producing an equilibrium configuration with an intrinsic toroidal topology. Examples of such solutions are the black rings in higher dimensional general relativity and the vortons in some classical field theory models formulated in a four dimensional flat spacetime. In this project we intend to investigate the analogy between black rings and vortons beyond this simple heuristic construction. This will result in a black ring-vorton ‘dictionary’, leading to a better understanding of both types of configurations, and to the discovery of new solutions. In particular, this analogy suggests the existence of composite multi-solitons describing ‘Saturns’ and ‘di-vortons’, which we intend to find. We also plan to study whether the centrifugal force can be replaced by the electromagnetic interaction to achieve equilibrium. By constructing both black rings and vortons with a cosmological constant, we will answer the question on how a non-asymptotically flat structure of spacetime affects solutions with ring topology.