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Bi-axisymmetric stationary solutions to the vacuum Einstein equation with non-spherical horizons

Banff International Research Station for Mathematical Innovation and Discovery

In the last 15 years, there has been much progress on higher dimensional solutions to the Einstein equation, much of it from the physics community. They are particularly interesting as, unlike 4 dimensional spacetimes, the horizon is no longer restricted to being diffeomorphic to the sphere, as demonstrated by the celebrated black ring solution of Emparan and Reall. Using the Weyl-Papapetrou coordinates and harmonic map, we show the existence of stationary solutions to the 5 dimensional vacuum Einstein equation, which are bi-axisymmetric solutions with lens space horizons. This is a joint project with Marcus Khuri and Gilbert Weinstein.

Mathematics; Relativity and gravitational theory; Differential geometry

video/mp4

Author affiliation: Gakushuin University

2017-02-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60370

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/