Journal
GENERAL RELATIVITY AND GRAVITATION
Volume 50, Issue 6, Pages -Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10714-018-2376-2
Keywords
Permeability tensor; Permittivity tensor; Magneto-electric tensor; Constitutive tensor; Susceptibility tensor; Effective metric; Analogue spacetime; Compatibility conditions
Funding
- Marsden Fund
- Victoria University of Wellington Ph.D. Scholarship
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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.
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