RADIATIVE EINSTEIN-MAXWELL SPACETIMES AND NO-HAIR THEOREMS

Friedrich's construction of purely radiative solutions out of static, asymptotically flat solutions of Einstein's vacuum equations is generalized to the Einstein-Maxwell case. These radiative solutions can be considered as being conformal and analytic extensions, to neighbourhoods of infinity, of local solutions to a certain time-symmetric initial value problem. We point out that the non-existence of non-trivial global solutions to the corresponding constraints provides the basis for known uniqueness proofs for static, asymptotically flat black-hole and perfect-fluid solutions. We also obtain a uniqueness theorem for static, charged perfect fluids whose equation of state belongs to a certain one-parameter family.