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We construct new complete, compact, inhomogeneous Einstein metrics on Sm+2 sphere bundles over 2n-dimensional Einstein–Kähler spaces K2n, for all n⩾1 and all m⩾1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of Sm with S2 bundles over K2n, for m>1. Additionally, we construct new complete, non-compact Ricci-flat metrics with topologies Sm times R2 bundles over K2n that generalise the higher-dimensional Taub-BOLT metrics, and with topologies Sm×R2n+2 that generalise the higher-dimensional Taub-NUT metrics, again for m>1. [Copyright &y& Elsevier]

Abstract: Using a novel numerical spectral method, we have constructed an – solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. This method is independent of the Ricci–DeTurck-flow method used by Figueras, Lucietti, and Wiseman. We have perturbed the solution to get large static black hole solutions to the Randall–Sundrum II (RSII) braneworld model. Our solution agrees closely with that of Figueras et al. and also allows us to deduce the new results that to first order in , the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about . [Copyright &y& Elsevier]