# Rotating black hole solutions in relativistic analogue gravity

## TL;DR

This paper investigates the potential of relativistic analogue gravity systems to simulate rotating black holes, specifically Kerr black holes, by establishing relations with non-relativistic solutions and introducing new vortex solutions for experimental and simulation purposes.

## Contribution

It introduces a new class of vortex solutions in relativistic systems and establishes a relation between relativistic and non-relativistic black hole solutions for analogue gravity.

## Key findings

- Established a relation between relativistic and non-relativistic solutions.
- Proposed new vortex solutions for relativistic analogue gravity.
- Suggested applications in simulations and experiments.

## Abstract

Simulation and experimental realization of acoustic black holes in analogue gravity systems have lead to a novel understanding of relevant phenomena such as Hawking radiation or superradiance. We explore here the possibility to use relativistic systems for simulating rotating black hole solutions and possibly get an acoustic analogue of a Kerr black hole. In doing so we demonstrate a precise relation between non-relativistic and relativistic solutions and provide a new class of vortex solutions for relativistic systems. Such solutions might be used in the future as a test bed in numerical simulations as well as concrete experiments.