Don N. Page

The general Kerr–de Sitter metrics in all dimensions

We give the general Kerr–de Sitter metric in arbitrary space–time dimension D≥4, with the maximal number [(D−1)/2] of independent rotation parameters. We obtain the metric in Kerr–Schild form, where it is written as the sum of a de Sitter metric plus the square of a null-geodesic vector, and in generalised Boyer–Lindquist coordinates. The Kerr–Schild form is simpler for verifying that the Einstein equations are satisfied, and we have explicitly checked our results for all dimensions D≤11. We discuss the global structure of the metrics, and obtain formulae for the surface gravities and areas of the event horizons. We also obtain the Euclidean-signature solutions, and we construct complete non-singular compact Einstein spaces on associated SD−2 bundles over S2, infinitely many for each odd D≥5.

New Einstein-Sasaki Spaces in Five and Higher Dimensions

We obtain infinite classes of new Einstein-Sasaki metrics on complete and nonsingular manifolds. They arise, after Euclideanization, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces L(p,q,r) in five dimensions have cohomogeneity 2 and U(1) x U(1) x U(1) isometry group. They are topologically S(2) x S(3). Their AdS/CFT duals describe quiver theories on the four-dimensional boundary of AdS(5). We also obtain new Einstein-Sasaki spaces of cohomogeneity n in all odd dimensions D = 2n + 1 > or = 5, with U(1)(n + 1) isometry.

Rotating black holes in higher dimensions with a cosmological constant

We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and the Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated S(D-2) bundles over S2, infinitely many for each odd D>/=5. Applications to string theory and M-theory are indicated.

Hawking radiation and black hole thermodynamics

An inexhaustive review of Hawking radiation and black hole thermodynamics is given, focusing especially upon some of the historical aspects as seen from the biased viewpoint of a minor player in the field on and off for the past 30 years.

New inhomogeneous Einstein metrics on sphere bundles over Einstein-Kähler manifolds

Abstract We construct new complete, compact, inhomogeneous Einstein metrics on S m +2 sphere bundles over 2 n -dimensional Einstein–Kahler spaces K 2 n , for all n ⩾1 and all m ⩾1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of S m with S 2 bundles over K 2 n , for m >1. Additionally, we construct new complete, non-compact Ricci-flat metrics with topologies S m times R 2 bundles over K 2 n that generalise the higher-dimensional Taub-BOLT metrics, and with topologies S m × R 2n+2 that generalise the higher-dimensional Taub-NUT metrics, again for m >1.

Anthropic estimates of the charge and mass of the proton

Abstract By combining a renormalization group argument relating the charge e and mass m p of the proton by e 2 ln m p ≈ − 0.1 π (in Planck units) with the Carter–Carr–Rees anthropic argument that gives an independent approximate relation m p ∼ e 20 between these two constants, both can be crudely estimated. These equations have the factor of 0.1 π and the exponent of 20 which depend upon known discrete parameters (e.g., the number of generations of quarks and leptons, and the number of spatial dimensions), but they contain no continuous observed parameters. Their solution gives the charge of the proton correct to within about 8%, though the mass estimate is off by a factor of about 1000 (16% error on a logarithmic scale). When one adds a fudge factor of 10 previously given by Carr and Rees, the agreement for the charge is within about 2%, and the mass is off by a factor of about 3 (2.4% error on a logarithmic scale). If this 10 were replaced by 15, the charge agrees within 1.1% and the mass itself agrees within 0.7%.