Spontaneous oscillations of the emission spectrum of a multimode wide-band laser

Abstract

In this paper dl vacuum metrics with a four-parameter homothety group containing a threpdimensional Abelian subpoup are found. These include the Kssner family of metrics, metriw related to the Kaener family by complex transformations (which include a family of vacuum metrics found by Lewis in 1932 and a metric found by Petmv in 1962 to be the only vacuum metric which admits a simplytransitive fou~parameta isometry group), together with algebraic+ degenerate van Stodnun, ppwave and plane-wave metrics. Apart from the plan,wave metric, all the 0th5 metric6 are written here as one general family.