Hyperbolic metamaterials and massive Klein-Gordon equation in (2+1)-dimensional de Sitter spacetime

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PHYSICAL REVIEW D, vol.104, no.9, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 104 Issue: 9
  • Publication Date: 2021
  • Doi Number: 10.1103/physrevd.104.105004
  • Journal Name: PHYSICAL REVIEW D
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Chemical Abstracts Core, INSPEC, zbMATH
  • Middle East Technical University Affiliated: Yes


The wave equation obeyed by the extraordinary component of the electric field in a hyperbolic metamaterial was shown to be a massless Klein-Gordon field living in a flat spacetime with two timelike and two spacelike dimensions. Such a wave equation, unexpectedly, allows dispersionless propagation albeit having two spatial dimensions. Here we show that the same equation can be naturally interpreted as a particular massive Klein-Gordon equation with the usual one timelike and two spacelike dimensions in a de Sitter (dS) background spacetime. The mass parameter of the scalar field is given in terms of the cosmological constant, Planck constant, and the speed of light as m = root Lambda(h) over bar /c which corresponds to the point for which the left and right conformal weights of the boundary conformal field theory (CFT) (via the de Sitter/CFT correspondence) are equal. This particular mass corresponds to the gapless mode in the dS spacetime for which the dispersion relation is linear in the wave number.