Yang-Mills Solutions on Euclidean Schwarzschild Space

Abstract

We show that the apparently periodic Charap-Duff Yang-Mills `instantons' in time-compactified Euclidean Schwarzschild space are actually time independent. For these solutions, the Yang-Mills potential is constant along the time direction (no barrier) and therefore, there is no tunneling. We also demonstrate that the solutions found to date are three dimensional monopoles and dyons. We conjecture that there are no time-dependent solutions in the Euclidean Schwarzschild background.