The hidden symmetries of multi-centre metrics
type: Item
instance of: scholarly article
title: The hidden symmetries of multi-centre metrics
zbMATH Open document ID: 0684.53074
DOI: 10.1007/BF01466773
author: P. Ruback
author: Gary W. Gibbons
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: This paper is chiefly concerned with the 4-dimensional positive definite Taub-NUT metric, which is relevant to problems in monopole physics. It is shown that this metric ``sits at the intersection of three families of Ricci-flat metrics'', which are discussed in some detail. Thereupon, its symmetries and the corresponding constants of motion of the geodesic equation are investigated. In particular, it is shown that there is a sort of ``hidden symmetry'' giving rise to an analogue of the classical Runge-Lenz vector. Finally, the results are applied to the scattering of BPS monopoles and fluctuations around such monopoles. This is a rather detailed account which presents both new and already known results in a homogeneous manner. As a minor correction, this reviewer would like to remark that Theorem 2.1 does not hold near a zero of the Killing vector field. Correspondingly, Theorem 2.3 has to be modified a little bit.
reviewed by: Volker Perlick
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 83C47
zbMATH DE Number: 4120976
zbMATH Keywords: Kähler metrics
zbMATH Keywords: Killing-Yano tensors
zbMATH Keywords: Atiyah-Hitchin metric
zbMATH Keywords: quantum field theory
zbMATH Keywords: Taub-NUT metric
zbMATH Keywords: hidden symmetry
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01466773
OpenAlex ID: W1965768031
description: scientific article; zbMATH DE number 4120976