Structure of plane gravitational waves of nonmetricity in affine-metric space

A definition of an affine-metric space of the plane wave type is given using the analogy with the properties of plane electromagnetic waves in Minkowski space. The action of the Lie derivative on the 40 components of the nonmetricity 1-form in the 4-dimensional affine-metric space leads to the conclusion that the nonmetricity of a plane wave type is determined by five arbitrary functions of delayed time. A theorem is proved that parts of the nonmetricity 1-form irreducible with respect to the Lorentz transformations of the tangent space, such as the Weyl 1-form, the trace 1-form, and the spin 3 1-form, are defined by one arbitrary function each, and the spin 2 1-form is defined by two arbitrary functions. This proves the possibility of transmitting information with the help of nonmetricity waves. © 2018 IOP Publishing Ltd