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Коллоквиум. Einstein, Weyl, and Five-Dimensional Blackhole Spacetime

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In 1917, shortly after Einstein had announced his master equation on the general relativity, H. Weyl characterized the Schwarzschild metric, which is the first nontrivial solution to the Einstein equation, by a harmonic function. Since then, the solutions to the Einstein equation with a certain set of symmetries are identified with elliptic variational problems, in particular the harmonic map equation, often called nonlinear sigma model. With Marcus Khuri and Gilbert Weinstein, we constructed a new set of stationary solutions to the 5-dimensional vacuum Einstein equation, which contains non-spherical event horizons, such as lens spaces. The higher dimensional spacetime exhibit a wider range of topological structures, compared to our 4-dimensional physical spacetime, and those stationary solutions are thus geometrically interesting.