Bespoke analogue space-times: Meta-material mimics

TL;DR

This paper explores how advanced meta-materials can mimic black-hole spacetimes by designing electromagnetic media with specific properties, revealing divergences at horizons and ergosurfaces, thus enabling laboratory analogues of gravitational phenomena.

Contribution

It demonstrates how to construct meta-materials that replicate various black-hole spacetimes, including Schwarzschild and Kerr, at the wave optics level, linking general relativity with material design.

Findings

Eigenvalues diverge at horizons in static black holes

Eigenvalues diverge at ergosurfaces in stationary black holes

Meta-material susceptibilities can model black-hole geometries

Abstract

Modern meta-materials allow one to construct electromagnetic media with almost arbitrary bespoke permittivity, permeability, and magneto-electric tensors. If (and only if) the permittivity, permeability, and magneto-electric tensors satisfy certain stringent compatibility conditions, can the meta-material be fully described (at the wave optics level) in terms of an effective Lorentzian metric --- an analogue spacetime. We shall consider some of the standard black-hole spacetimes of primary interest in general relativity, in various coordinate systems, and determine the equivalent meta-material susceptibility tensors in a laboratory setting. In static black hole spacetimes (Schwarzschild and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the horizon. In stationary black hole spacetimes (Kerr and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the ergo-surface.