Surface densities in General Relativity

TL;DR

This paper develops a method to construct surface densities for angular momentum in asymptotically flat, stationary, axisymmetric spacetimes, applying it to the Kerr metric to obtain a regularized density representation.

Contribution

It introduces a new approach to define integrable surface densities for angular momentum, addressing discontinuities in the twist potential in General Relativity.

Findings

Derived a regularized angular momentum density for Kerr spacetime

Provided a formalism for constructing surface densities from discontinuities

Applied the method to obtain an integrable density in specific spacetimes

Abstract

In this lecture we deal with the construction of surface densities for the angular momentum of the sources of asymptotically flat vacuum stationary axisymmetric spacetimes. These sources arise from the discontinuities of the twist potential. The result will be applied to the Kerr metric to obtain an integrable density which can be viewed as the regularized version of the density obtained using other formalisms.