A Periodic Analog of the Schwarzschild Solution

We construct a new exact solution of Einstein’s equations in vacuo in terms of Weyl canonical coordinates. This solution may be interpreted as a black hole in a space-time which is periodic in one direction and which behaves asymptotically like the Kasner solution with Kasner index equal to $4M{L}^{-1}$, where $L$ is the period and $M$ is the mass of the black hole. Outside the horizon, the solution is free of singularities and approaches the Schwarzschild solution as $L\to \mathrm{\infty }$.