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

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.