Properties of some five dimensional Einstein metrics

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.

1+43 pages, 2 figures, LaTeX. Minor typos corrected

References in corpus (9)

• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• Einstein manifolds and conformal field theories
• Gravitational instability in higher dimensions
• Towards the Final Fate of an Unstable Black String
• Bohm and Einstein-Sasaki Metrics, Black Holes and Cosmological Event Horizons
• Stability of AdS_p x M_q Compactifications Without Supersymmetry
• Some interesting violations of the Breitenlohner-Freedman bound
• Instability of generalised AdS black holes and thermal field theory
• Casimir effect and thermodynamics of horizon instabilities

Cited by in corpus (8)

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• Supersymmetric solutions for non-relativistic holography
• Scalar Laplacian on Sasaki-Einstein Manifolds Y^{p,q}
• Quantum integrability of quadratic Killing tensors
• Lovelock black holes with nonmaximally symmetric horizons
• New solutions of exotic charged black holes and their stability
• New non compact Calabi-Yau metrics in D=6
• Complete Calabi-Yau metrics from Kahler metrics in D=4