Non-singular, vacuum, stationary space-times with a negative cosmological constant

We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant.Comment: minor corrections, an inessential uniqueness claim withdraw

Conformally covariant parameterizations for relativistic initial data

We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parameterization is certainly more natural for non constant mean curvature initial data

Non-singular spacetimes with a negative cosmological constant: III. Stationary solutions with matter fields

Generalising the results in arXiv:1612.00281, we construct infinite-dimensional families of non-singular stationary space times, solutions of Yang-Mills-Higgs-Einstein-Maxwell-Chern-Simons-dilaton-scalar field equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.Comment: 27 pages, v2: journal accepted versio

Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields

We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$ equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.Comment: 16 pages, journal accepted versio

Manifold structures for sets of solutions of the general relativistic constraint equations

We construct manifold structures on various sets of solutions of the general relativistic initial data sets.Comment: latex2e, 32 A4 pages, minor correction