Global monopoles and scalar fields as the electrogravity dual of Schwarzschild spacetime

We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, $T_0^0-T_i^i=0$. This property was however known for the global monopole spacetime while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos - Zannias scalar field solution is dual to flat space.