Black Rings, Vortons and Saturns: a `Dictionary´

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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.