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The Optical Metric was defined by German theoretical physicist Walter Gordon in 1923 〔W. Gordon, 1923, Annals of Physics (New York), 22, 421〕 to study the geometrical optics in curved space-time filled with moving dielectric materials. Let be the normalized (covariant) 4-velocity of the arbitrarily-moving dielectric medium filling the space-time, and assume that the fluid’s electromagnetic properties are linear, isotropic, transparent, nondispersive, and can be summarized by two scalar functions: a dielectric permittivity ε and a magnetic permeability μ.〔J. D. Jackson, "Classical Electrodynamics", 1998, (John Wiley & Sons Inc, New York)〕 Then optical metric tensor is defined as , where is the physical metric tensor. The inverse (contravariant) optical metric tensor is , where is the contravariant 4-velocity of the moving fluid. Note that the traditional refractive index is defined as . == Properties == An important fact about Gordon's optical metric is that in curved space-time filled with dielectric material, electromagnetic waves (under geometrical optics approximation) follows geodesics of the optical metric instead of the physical metric. Consequently, the study of geometric optics in curved space-time with dielectric material can sometimes be simplified by using optical metric (note that the dynamics of the physical system is still described by the physical metric). For example, optical metric can be used to study the radiative transfer in stellar atmospheres around compact astrophysical objects such as neutron stars and white dwarfs, and in accretion disks around black holes.〔J. I. Castor, ''Radiation Hydrodynamics'', 2007, (Cambridge University Press, Cambridge)〕 In cosmology, optical metric can be used to study the distance-redshift relation in cosmological models in which the intergalactic or interstellar medium have a non-vanishing refraction index. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Optical metric」の詳細全文を読む スポンサード リンク
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