Negative mass scenario and Schwarzschild spacetime in general relativity

TL;DR

This paper explores the theoretical implications of negative mass in Schwarzschild spacetime, showing that mass inversion relates different regions of the spacetime through discrete transformations, potentially unifying positive and negative mass regions.

Contribution

It demonstrates that mass inversion in Schwarzschild spacetime corresponds to coordinate inversion in Kruskal-Szekeres coordinates, suggesting a unified description of positive and negative mass regions.

Findings

Mass inversion corresponds to coordinate inversion in Kruskal-Szekeres coordinates.

Schwarzschild spacetime can be described by interconnected regions of positive and negative masses.

Discrete PT transformations relate different regions of the spacetime.

Abstract

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.