Einstein spaces

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Einstein: "Relativity and the Problem of Space"

Permissions Icon Permissions. Abstract In terms of Eddington-Finkelstein coordinates, we give the most general form of the line element for all type D empty spaces.

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  4. Self-dual Einstein Spaces, Heavenly Metrics and Twistors?
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    Einstein Was Right: Space-Time Is Smooth, Not Foamy

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    Abstract : Four-dimensional quaternion-Kahler metrics, or equivalently self-dual Einstein spaces M, are known to be encoded locally into one real function h subject to Przanowski's Heavenly equation. We elucidate the relation between this description and the usual twistor description for quaternion-Kahler spaces. In particular, we show that the same space M can be described by infinitely many different solutions h, associated to different complex local submanifolds on the twistor space, and therefore to different local integrable complex structures on M. We also study quaternion-Kahler deformations of M and, in the special case where M has a Killing vector field, show that the corresponding variations of h are related to eigenmodes of the conformal Laplacian on M.

    Einstein made an unbelievable prediction 100 years ago