Construction of a Penrose Diagram for an Accreting Black Hole

TL;DR

This paper constructs a Penrose diagram for an accreting black hole, illustrating its causal structure and features like horizons and singularities, based on a stepwise steady accretion model.

Contribution

It presents a novel method to construct a Penrose diagram for an accreting black hole with stepwise steady rates, including coordinate derivation and feature verification.

Findings

Coordinate lines derived computationally

Horizon and mass scale dependencies demonstrated

Singularity onset reveals new spacetime region

Abstract

A Penrose diagram is constructed for a spatially coherent black hole that accretes at stepwise steady rates as measured by a distant observer from an initial state described by a metric of Minkowski form. Coordinate lines are computationally derived, and radial light-like trajectories verify the viability of the diagram. Coordinate dependencies of significant features, such as the horizon and radial mass scale, are clearly demonstrated on the diagram. The onset of a singularity at the origin is shown to open a new region in space-time that contains the interior of the black hole.