The spacetime in the neighborhood of a general isolated black hole

TL;DR

This paper develops a detailed mathematical model of the spacetime structure near a general isolated black hole, incorporating rotation and charge, using a power series expansion in a characteristic initial value framework.

Contribution

It introduces a novel approach to modeling near-horizon geometry of isolated black holes with rotation and charge using the Newman-Penrose formalism and characteristic initial value formulation.

Findings

First detailed power series expansion of near-horizon spacetime

Framework applicable to rotating and charged black holes

Lays groundwork for future physical applications

Abstract

We construct the spacetime in the vicinity of a general isolated, rotating, charged black hole. The black hole is modeled as a weakly isolated horizon, and we use the characteristic initial value formulation of the Einstein equations with the horizon as an inner boundary. The spacetime metric and other geometric fields are expanded in a power series in a radial coordinate away from the horizon by solving the characteristic field equations in the Newman-Penrose formalism. This is the first in a series of papers which investigate the near horizon geometry and its physical applications using the isolated horizon framework.