Analyticity of strictly static and strictly stationary, inheriting and non-inheriting Einstein-Maxwell solutions

Following the technique of M\"uller-zum-Hagen, refs [1,2], we show that strictly static and strictly stationary solutions of the Einstein-Maxwell equations are analytic in harmonic coordinates. This holds whether or not the Maxwell field inherits the symmetry.Comment: 11 pages; to appear in Gen.Rel.Gra

Valiente Kroon's obstructions to smoothness at infinity

We conjecture an interpretation in terms of multipole moments of the obstructions to smoothness at infinity found for time-symmetric, conformally-flat initial data by Valiente Kroon (Comm. Math. Phys. 244 (2004), 133-156).Comment: To appear in GR

Einstein--Weyl spaces and dispersionless Kadomtsev--Petviashvili equation from Painlev\'e I and II

We present two constructions of new solutions to the dispersionless KP (dKP) equation arising from the first two Painlev\'e transcendents. The first construction is a hodograph transformation based on Einstein--Weyl geometry, the generalised Nahm's equation and the isomonodromy problem. The second construction, motivated by the first, is a direct characterisation of solutions to dKP which are constant on a central quadric. We show how the solutions to the dKP equations can be used to construct some three-dimensional Einstein--Weyl structures, and four--dimensional anti-self-dual null-K\"ahler metrics.Comment: Final version, to be published in Physics Letters