Exact four-parameter rotating NS-NS vacuum in double field theory

A bstract We construct an exact rotating vacuum of the NS-NS sector, equivalently a Double Field Theory vacuum. The construction applies compact SO (2) S-duality to a rotating Einstein-scalar seed. The solution has four independent parameters ,j,q,ζ \ m j q ζ . To our knowledge, this is the first explicit rotating solution of the pure NS-NS vacuum equations with all three NS-NS fields { g , B , ϕ } determined analytically, independent dilaton and H -flux charges, and no Maxwell sector. The static limit is obtained by taking the rotation parameter j → 0. In this limit the geometry is not the spherical Burgess-Myers-Quevedo solution. Instead, it is an axial Zipoy-Voorhees branch carrying H -flux, so an oblate deformation remains after rotation is switched off. This geometric memory is absent in pure general relativity and in Einstein-Maxwell-dilaton-axion. The two static branches nevertheless share the same ℓ = 0 parametrized post-Newtonian data { MG , β PPN , γ PPN , h }. They give two inequivalent NS-NS geometries at identical monopole charges, with the degeneracy lifted at ℓ = 2. At the Kerr horizon locus the outer shell is generically singular in curvature. Above the threshold |q|>√m²-j² q > m 2 − j 2 , polar geodesics are repelled outward and the rotation axis becomes regular in curvature at the shell. On that axis the inverse metric g μν stays finite while the lower-index Riemannian metric components diverge, whereas off the axis the inverse metric itself diverges. This axis-local degeneracy may offer a setting for non-Riemannian geometry in Double Field Theory, where g μν is not fundamental and the O ( D , D ) variables ,HAB\ d H AB remain well defined.