Initial data for a deformed isolated horizon

TL;DR

This paper constructs initial data for deformed isolated horizons in axisymmetric black hole spacetimes, illustrating the effects of matter, like accretion disks, on horizon geometry using analytical and numerical methods.

Contribution

It introduces a method to generate initial data for deformed black hole horizons within the isolated horizon formalism, including numerical solutions for accretion disk effects.

Findings

Constructed initial data for deformed isolated horizons.

Numerical solution for a black hole with an accretion disk.

Analyzed how matter influences horizon geometry.

Abstract

Within the isolated horizon formalism, we investigate a static axisymmetric space-time of a black hole influenced by matter in its neighborhood. To illustrate the role of ingredients and assumptions in this formalism, we first show how, in spherical symmetry, the field equations and gauge conditions imply the isolated horizon initial data leading to the Schwarzschild space-time. Then, we construct the initial data for a static axisymmetric isolated horizon representing a deformed black hole. The space-time description in the Bondi-like coordinates is then found as a series expansion in the vicinity of the horizon. To graphically illustrate this construction, we also find a numerical solution for a black hole deformed by a particular analytic model of a thin accretion disk. We also discuss how an accretion disk affects the analytical properties of the horizon geometry.