Describing Lorentz transformations, Doppler's effect, Hubble's law, and others in curvilinear coordinates using generalized biquaternions

The paper presents the derivation of Lorentz transformations in curvilinear coordinates using a generalized biquaternions method. The orbital rotation of the source and/or receiver, i.e. (mathematically) the Lorentz transformation in spherical coordinates, is the cause of the transverse Doppler effect. The change of the wave frequency, i.e., «redshift” leads to nonlinearities of Hubble's law, e.g., accelerated and anisotropic expansion of the Universe, aberration, and wave polarization.