Stability of the intrinsic energy vanishing in the Schwarzschild metric under a slow rotation

TL;DR

This paper demonstrates that the intrinsic energy vanishing property of the Schwarzschild metric remains stable when subjected to slow rotational perturbations, as shown through analysis of the linearized Kerr metric in intrinsic coordinates.

Contribution

It shows that the zero-energy property of Schwarzschild spacetime is preserved under slow rotation by analyzing the linearized Kerr metric in intrinsic coordinates.

Findings

The linear and angular 4-momenta are zero in intrinsic coordinates.

The zero-energy property of Schwarzschild remains stable under slow rotation.

The analysis uses Gauss coordinates adapted to the linearized Kerr metric.

Abstract

The linearized Kerr metric is considered and put in some Gauss coordinates which are further {\em intrinsic} ones. The linear and angular 4-momenta of this metric are calculated in these coordinates and the resulting value is just zero. Thus, the global vanishing previously found for the Schwarzschild metric remains linearly stable under slow rotational perturbations of this metric.