Estimation of the Birefringence Change in Crystals Induced by Gravitation Field

1 Estimation of the Birefringence Change in Crystals Induced by Gravitation Field R.Vlokh and M.Kostyrko Institute of Physical Optics, 23 Dragomanov St., 79005 Lviv, Ukraine, e-mail: vlokh@ifo.lviv.ua Received: 19.08.2005 Abstract The effect of gravitation field of spherically symmetric mass on the birefringent properties of crystals has been analysed. It has been shown that the gravitation field with spherical symmetry can lead to a change of birefringence in anisotropic media. Keywords: gravitation field, birefringence, crystal optics, symmetry PACS: 42.25.Lc, 78.20.Ci, 04.20.Cv Introduction It has been shown in our previous work (see R. Vlokh [1]) that the gravitation field of spherically symmetric mass cannot induce lowering of symmetry of space or polarizable vacuum and appearance of its optical anisotropy. This conclusion has been based on the relations for the refraction index n (or the dielectric impermeability constant ( ) 2 1 ij ij B n = ) changes under the action of gravitation field of spherically symmetric mass, derived in the weak-field approximation: 1/ 2 1 2 ( ) ij n M g β = + ,

(1) 1/ 2 1 4 ( ) ij ij B M g β = − .

(2) Here 4 0 ij G c β = , 0c is the light speed in vacuum and G the gravitation constant. Namely, the square root of the gravitation field strength (the so-called free-fall acceleration), 1/ 2 g , describes a scalar action which cannot lower symmetry of a medium. Many authors have already considered light propagation in a flat space near a massive body, basing on the idea of distributed dielectric permittivity (or refractive index) of the space treated as a matter. For instance, R.H. Dicke has done this on the basis of Newton and Maxwell equations (see, e.g., [2]), H.E. Puthoff [3] has considered the phenomena analysed usually in terms of curved space-time, using the approach of polarizable vacuum, while K. Nandi and A. Islam [4], J. Evans [5] and Fernando de Felice [6] have treated optical phenomena in the gravitation field on the basis of “optical-mechanical analogy”. Recently P. Boonserm et al. [7] have found that the internal stresses in celestial bodies can lead to appearance of the corresponding optical anisotropy and so a necessity for introduction of “effective refractive index tensor”. According to this approach, the refraction index can acquire properties of a second-rank tensor, provided that certain conditions are imposed on the gravitation field. It is necessary to emphasize that the refractive index is not a tensorial quantity, unlike the optical-frequency dielectric impermeability constant, which represents a two-rank tensor. It follows from Eqs. (1) and (2) of the study [1]

2 that the light speed depends upon the gravitation field and approaches the c0 value only if the field strength tends to zero. The G quantity represents in fact material (constitutive) coefficients of the flat space (or the corresponding optical medium) and should therefore obey the Neumann principle. Being a scalar action, gravitation field of a spherical mass cannot lead to appearance of anisotropy. In case of hypothetical lowering of initially isotropic symmetry of space by the gravitation or the other fields, the coefficient G, the Hubble constant and the time can get tensorial properties. In frame of this description, the time plays a role of spatial property. Owing to the Curie principle, the symmetry group of the flat space should depend on the field configuration and, following the Neumann symmetry principle, it should be a subgroup of symmetry group of the time. Then the following questions appear: if the gravitation field of spherically symmetric mass induces refractive index change for the “free space” or the polarizable vacuum, could this field change refraction indices of the other types of matter, for example, anisotropic crystals? Furthermore, could the optical birefringence of anisotropic media be sensitive to the changes in the gravitation field of spherical symmetry? Dependence of birefringence on the gravitation field At present, measurements of changes in the absolute refractive index values of the order of 10-5 are a difficult experimental problem. Nonetheless, the methods for experimental determination of the birefringence changes are more sensitive. For instance, a usual compensation method for measuring the birefringence permits one to detect its increment of the order of 10-7. As we have mentioned above, the gravitation field, as a scalar action, does not induce the optical anisotropy for itself. Thus the question should be made more specific: does it induce any changes of optical anisotropy? Let us follow from Eq. (2) and present the optical indicatrix equation for the crystals of medium symmetry (i.e., those belonging to trigonal, tetragonal and hexagonal symmetry groups) under the perturbation induced by scalar action

This content is AI-processed based on open access ArXiv data.