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arXiv · hep-th/0407030

Properties of some five dimensional Einstein metrics

Gary W. Gibbons·Sean A. Hartnoll·Yukinori Yasui
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Abstract

The volumes, spectra and geodesics of a recently constructed infinite family of five-dimensional inhomogeneous Einstein metrics on the two $S^3$ bundles over $S^2$ are examined. The metrics are in general of cohomogeneity one but they contain the infinite family of homogeneous metrics $T^{p,1}$. The geodesic flow is shown to be completely integrable, in fact both the Hamilton-Jacobi and the Laplace equation separate. As an application of these results, we compute the zeta function of the Laplace operator on $T^{p,1}$ for large $p$. We discuss the spectrum of the Lichnerowicz operator on symmetric transverse tracefree second rank tensor fields, with application to the stability of Freund-Rubin compactifications and generalised black holes.

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Gary W. Gibbons, Sean A. Hartnoll, Yukinori Yasui. 2005-02-19. Properties of some five dimensional Einstein metrics. https://doi.org/10.1088/0264-9381%2F21%2F19%2F014

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