Nonmetricity plane waves in post Riemannian spacetime

Using the analogy with the properties of plane electromagnetic waves in Minkowski space, a definition of an affine-metric space of the plane wave type is given, which is characterized by the null action of the Lie derivative on the 40 components of the nonmetricity 1-form in the 4-dimensional affine-metric space. This leads to the conclusion that the nonmetricity of a plane wave type is determined by five arbitrary functions of delayed time. A theorem on the structure of the nonmetricity of the plane wave type is proved, which states 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 symmetric 1-form, are defined by one arbitrary function each, and the antisymmetric 1-form is defined by two arbitrary functions. Presence of arbitrary functions in the description of nonmetricity plane waves allows transmitting information with the help of nonmetricity waves. © Published under licence by IOP Publishing Ltd.