R. Beig, S. Husa
Initial Data with Toroidal Conformal Symmetry
The paper is published: Phys.Rev.D 50 (1994) 7116-7118
PACS: 4.20.Ex
Abstract: A new class of time-symmetric solutions to the initial value constraints of
vacuum General Relativity is introduced. These data are globally regular,
asymptotically flat (with possibly several asymptotic ends) and in general
have no isometries, but a $U(1)\times U(1)$ group of conformal isometries.
After decomposing the Lichnerowicz conformal factor in a double Fourier series
on the group orbits, the solutions are given in terms of a countable family of
uncoupled ODEs on the orbit space.

Keywords: general relativity, initial value constraints, conformal isometry