One-parameter families of conformally related asymptotically flat, static vacuum data

Abstract

Extending the results of Friedrich (2008 Class. Quantum Grav. 25 065012) we give a complete description of the asymptotically flat, conformally non-flat, static vacuum data which admit non-trivial, asymptotically smooth conformal mappings onto other such data. These data form a 3-parameter family which decomposes into 1-parameter families of data which are conformal to each other. The data and the associated static vacuum solutions are given explicitly in terms of elliptic and, in a special case, elementary functions. © 2008 IOP Publishing Ltd.