  Original abstract: "We construct periodic solutions of nonlinear wave
equations using analytic continuation. The construction applies in particular
to Einstein equations, leading to infinite-dimensional families of
time-periodic solutions of the vacuum, or of the
Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$
equations, with a negative cosmological constant." However, there is a gap in
the proof, and it is unlikely that the strategy presented can be upgraded to a
full proof.
