Fluid analogs for rotating black holes

TL;DR

This paper explores fluid analog models for rotating black holes, extending previous work to curved and dynamic geometries, and provides new fluid descriptions for Kerr and BTZ black holes to aid visualization of their spacetime structures.

Contribution

It introduces novel fluid flow models on curved and time-dependent geometries for rotating black holes, enhancing understanding and visualization of complex spacetime solutions.

Findings

Fluid models for Kerr black holes using Doran coordinates.

Two fluid descriptions for spinning BTZ black holes.

Extension of fluid analogs to curved and dynamic geometries.

Abstract

Fluid analog models for gravity are based on the idea that any spacetime geometry admits a reinterpretation in which space is thought of as a fluid flowing with a prescribed velocity. This fluid picture is a restatement of the ADM decomposition of the metric. Most of the literature has focused on flat spatial geometries and physical fluid flows, with a view toward possible laboratory realizations. Here we relax these conditions and consider fluid flows on curved and time-dependent spatial geometries, as a way of understanding and visualizing solutions to general relativity. We illustrate the utility of the approach with rotating black holes. For the Kerr black hole we develop a fluid description based on Doran coordinates. For spinning BTZ black holes we develop two different fluid descriptions. One involves static conical spatial slices, with the fluid orbiting the tip of the cone. The other resembles a cosmology, with the fluid flowing on a time-dependent cylindrical geometry.