Black hole encircled by a thin disk: fully relativistic solution

TL;DR

This paper presents an exact, fully relativistic metric describing a static, axisymmetric thin disk around a Schwarzschild black hole, with realistic density profiles and analytical metric functions, enabling detailed study of such astrophysical systems.

Contribution

It provides the first fully analytical, regular metric solution for a black hole encircled by a thin disk with realistic density profiles, without edges or singularities.

Findings

The solution is expressed as finite Legendre polynomial series.

Disks have no edges and are regular outside the horizon.

Analytical metric functions facilitate detailed analysis of black hole–disk systems.

Abstract

We give a full metric describing the gravitational field of a static and axisymmetric thin disk without radial pressure encircling a Schwarzschild black hole. The disk density profiles are astrophysically realistic, stretching from the horizon to radial infinity, yet falling off quickly at both these locations. The metric functions are expressed as finite series of Legendre polynomials. Main advantages of the solution are that (i) the disks have no edges, so their fields are everywhere regular (outside the horizon), and that (ii) all non-trivial metric functions are provided analytically and in closed forms. We examine and illustrate basic properties of the black-hole -- disk space-times.