The general solution of Bianchi type VII\(_h\) vacuum cosmology (Q1016000)

A method developed by the authors in their previous works is used for study of Bianchi type \({VII}_{h}\) vacuum geometries. They re-derive a general vacuum solution of Bianchi type \({VII_0}\) and express it in terms of the third Painlevé transcendental. Though this family of metrics was already known, it was not known to be a general solution of this Bianchi type. General solution of Bianchi type VII\(_h\) is also implicitly given in terms of the sixth Painlevé transcendental. All six previously known solutions within this class are recovered and a new family of solutions is discovered.