Article

# New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes

02/2004; DOI:doi:10.1007/s00220-004-1225-1
Source: arXiv

ABSTRACT A new infinite series of Einstein metrics is constructed explicitly on S^2 x S^3, and the non-trivial S^3-bundle over S^2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional AdS Kerr black hole. In the special case, the metrics reduce to the homogeneous Einstein metrics studied by Wang and Ziller. We also construct an inhomogeneous Einstein metric on the non-trivial S^{d-2}-bundle over S^2 from a d-dimensional AdS Kerr black hole. Our construction is a higher dimensional version of the method of Page, which gave an inhomogeneous Einstein metric on CP^2\sharp\bar{CP^2}. Comment: 15 pages, remarks and minor corrections added

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##### Article:Examples of Einstein manifolds in odd dimensions
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ABSTRACT: We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kahler-Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat metrics have slower-than-Euclidean volume growth and quadratic curvature decay. Also we construct positive Einstein metrics on certain 3-sphere bundles over a Fano Kahler-Einstein manifold. We classify the homeomorphism and diffeomorphism types of the total spaces when the base is the complex projective plane.
03/2011;

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### Keywords

Einstein metrics

extreme 5-dimensional AdS Kerr black hole

homogeneous Einstein metrics

infinite numbers

inhomogeneous Einstein metric

inhomogeneous ones

minor corrections

new infinite series

non-trivial S^3-bundle

non-trivial S^{d-2}-bundle

remarks

special case