Angular Momentum Surface Density of the Kerr Metric
L. Fernandez-Jambrina, F.J. Chinea
TL;DR
This paper introduces a method to interpret angular momentum surface densities in the Kerr metric, ensuring the total angular momentum integral is finite, and provides a regularized density consistent with other approaches.
Contribution
A novel formalism for deriving finite, regularized angular momentum surface densities in the Kerr metric from vacuum stationary axisymmetric solutions.
Findings
Total angular momentum integral is finite for Kerr
Derived a regularized surface density consistent with previous methods
Provided a new interpretation of twist potential discontinuities
Abstract
A method for interpreting discontinuities of the twist potential of vacuum stationary axisymmetric solutions of Einstein's equations is introduced. Surface densities for the angular momentum of the source can be constructed after solving a linear partial differential equation with boundary conditions at infinity. This formalism is applied to the Kerr metric, obtaining a regularized version of the density calculated with other formalisms. The main result is that the integral defining the total angular momentum is finite for the Kerr metric.
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