K-Slicing the Reissner-Nordstrom Spacetime: Some New Observations

TL;DR

This paper develops a modified K-slicing method for Reissner-Nordstrom spacetimes, including the extreme case, improving previous approaches and analyzing the asymptotic behavior of the slicing.

Contribution

The authors introduce a new procedure for K-slicing that works for the extreme Reissner-Nordstrom case, extending previous methods and verifying accuracy and asymptotic properties.

Findings

Successfully extended K-slicing to the extreme RN case

Validated the method on Schwarzschild and RN metrics

Analyzed asymptotic behavior for large K

Abstract

There were problems encountered in extending the K-slicing of the Schwarzschild and Reissner-Nordstrom (RN) spacetimes [1, 2] to the extreme case, when charge equals mass (in gravitational units). The earlier procedure is here modified so as to allow us to obtain a K-slicing of the region outside the horizon of the extreme metric by spacelike hypersurfaces. We checked this new procedure by applying it to the Schwarzschild and usual RN metrics and recovering the previous foliation with an improved accuracy. We have also checked the asymptotic behaviour of the K-slicing for large K by extrapolation.