  We develop solution-generating techniques for stationary metrics with one
angular momentum and axial symmetry, in the presence of a cosmological constant
and in arbitrary spacetime dimension. In parallel we study the related lower
dimensional Einstein-Maxwell-dilaton static spacetimes with a Liouville
potential. For vanishing cosmological constant, we show that the field
equations in more than four dimensions decouple into a four dimensional
Papapetrou system and a Weyl system. We also show that given any four
dimensional 'seed' solution, one can construct an infinity of higher
dimensional solutions parametrised by the Weyl potentials, associated to the
extra dimensions. When the cosmological constant is non-zero, we discuss the
symmetries of the field equations, and then extend the well known works of
Papapetrou and Ernst (concerning the complex Ernst equation) in
four-dimensional general relativity, to arbitrary dimensions. In particular, we
demonstrate that the Papapetrou hypothesis generically reduces a stationary
system to a static one even in the presence of a cosmological constant. We also
give a particular class of solutions which are deformations of the (planar) adS
soliton and the (planar) adS black hole. We give example solutions of these
techniques and determine the four-dimensional seed solutions of the 5
dimensional black ring and the Myers-Perry black hole.

General Relativity and Quantum Cosmology;High Energy Physics - Theory