Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-07-05
Class.Quant.Grav.21:4697,2004
Physics
High Energy Physics
High Energy Physics - Theory
1+43 pages, 2 figures, LaTeX. Minor typos corrected
Scientific paper
10.1088/0264-9381/21/19/014
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.
Gibbons Gary W.
Hartnoll Sean A.
Yasui Yukinori
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