Active gravitational mass and the invariant characterization of Reissner-Nordstrom spacetime

TL;DR

This paper investigates the active gravitational mass in Reissner-Nordstrom spacetime using scalar invariants and the Karlhede classification, revealing which invariants correctly characterize the mass.

Contribution

It demonstrates that Weyl tensor invariants and Cartan scalars accurately represent the active gravitational mass, unlike the Kretschmann scalar.

Findings

Weyl tensor invariants match the expected active gravitational mass

Cartan scalars also correctly characterize the mass

Kretschmann scalar does not produce the expected mass expression

Abstract

We analyse the concept of active gravitational mass for Reissner-Nordstrom spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do.