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 $$ \left\{\mathfrak{m},j,\mathfrak{q},\zeta \right\} $$ 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 $$ \left|\mathfrak{q}\right|>\sqrt{{\mathfrak{m}}^2-{j}^2} $$ 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 $$ \left\{d,{\mathcal{H}}_{AB}\right\} $$ d H AB remain well defined.