This paper is available on arxiv under CC 4.0 license. Authors: (1) Igor Yu. Potemine, Institut de Math´ematiques, Universit´e Paul Sabatier. Table of Links Abstract and Introduction 5-dimensional Einstein Equations Nested Gogberashvili Models Harmony of Transcosmic Spheres Sequence of Event Horizons Time-amalgamated Multiverses Dark Energy and Multiversal Nurseries Black Holes as Multiverses Multi-solitonic and Gyratonic Gravitational Waves Elliptic and Spiral Galaxies Cosmological Coupling Conclusion and References 9 Multi-solitonic and gyratonic gravitational waves So, we are interested in Robinson-Trautman metrics describing expanding spacetimes with spherical gravitational waves. Multi-soliton solutions of this type, associated with matter trapping, correspond to our Gogberashvili multiverses. If we admit that the null matter field has some internal spin / angular momentum, there are also more general (multi-)gyratonic solutions. They give rise to rotating Gogberashvili models/multiverses. This intriguing topic, including a thorough comparison ot two models, should be studied in more details. In particular, the harmony of transcosmic spheres should acquire more complete meaning.