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Bespoke analogue space-times: meta-material mimics

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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.

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Notes

  1. To proceed, we could in principle perform a “local” Lorentz transformation from the rest frame V of the medium into the laboratory frame—along the lines of Appendix B of reference [1], but the “matching” analysis presented here is more straightforward.

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Acknowledgements

MV acknowledges financial support from the Marsden Fund administered by the Royal Society of New Zealand. SS was also supported by a Victoria University of Wellington Ph.D. Scholarship.

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  1. School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington, 6140, New Zealand

    Sebastian Schuster & Matt Visser

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Schuster, S., Visser, M. Bespoke analogue space-times: meta-material mimics. Gen Relativ Gravit 50, 55 (2018). https://doi.org/10.1007/s10714-018-2376-2

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