Hermann Weyl, in 1918, in his book "Space, Time, Matter" had written down the then-newly discovered Schwarzschild solution to the Einstein equation using cylindrical coordinates, and discovered that it is completely determined by a harmonic function. Over the next hundred years since, the Einstein equation has been associated to elliptic variational problems, often called the sigma-model approach. In a joint-work with Marcus Khuri and Gilbert Weinstein, we constructed a new set of 5-dimensional vacuum stationary Einstein metrics with a set of axial symmetries, and with 3-dimensional blackhole horizons which are not necessarily spherical. If time allows, we will present topological classification of the domains of outer communication thus constructed, in a joint-work with Yukio Matsumoto.