Negative mass scenario and Schwarzschild spacetime in general relativity

In this note we discuss the hypothesis of a presence of the negative mass in the Schwarzschild’s spacetime following to ideas of \cite{Villata,Chardin}. We demonstrate, that the discrete $PT$ transformation of the coordinates and mass inversion in the Schwarzschild’s metric solution is equivalent to the inversion of the Kruskal-Szekeres coordinates, \cite{Kruskal}, in the full region of the solution’s spacetime. As the consequence of the result, it is argued that the whole Schwarzschild spacetime can be described in terms of regions of positive and negative masses interconnected by the discrete transforms.