Negative mass scenario and Schwarzschild spacetime in general relativity

Abstract

In this note, we discuss the hypothesis of a presence of the negative mass matter in the Schwarzschild’s spacetime and 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 [M. D. Kruskal, Phys. Rev. 119, 1743 (1960); G. Szekeres, Publ. Mat. Debrecen 7, 285 (1960)], 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.