Insights into the Evolution of Horizons from Non-Orthogonal Temporal Coordinates

TL;DR

This paper explores how different coordinate systems, especially flowing river coordinates, affect the understanding of black hole horizons and their time evolution, avoiding singularities and providing a clearer depiction of black hole dynamics.

Contribution

It introduces a coordinate framework analogous to a flowing river to describe evolving black hole horizons, resolving singularities in traditional models.

Findings

Flowing river coordinates eliminate horizon singularities.

A Penrose diagram illustrates black hole growth and evaporation.

Coordinate anomalies are explained through this new framework.

Abstract

The introduction of coordinates representing the points of view of various observers results in the possibility of horizons when acceleration and gravitation are included. A horizon is a surface of possible light beams in a region of space of finite distance from the observer, which means that since nothing travels faster than light, events on the far side of a horizon cannot influence those on the causal side. A black hole has such a horizon, where some radially outgoing light beams can never reach a distant (or even nearby) observer. However, since one suspects that black holes can swallow energy, and even evaporate by Hawking radiation, such horizons must take on a time dependency. A naive introduction of temporal dependency results in infinities (singularities) in energy densities, suggesting in such descriptions that an in-falling observer would encounter a hard surface at the horizon. However, if coordinates representing space-time as analogous to a "flowing river" are used to describe the dynamics of a black hole, no such singularities are encountered. Such a parameterization of time dependent horizons will be offered in this presentation. A Penrose space-time diagram (which represents the entire space-time on a finite diagram with light beams always moving at a 45 degree angle to vertical) describing the growth and evaporation of an example black hole, along with the resulting coordinate anomaly, will be constructed.