A Generalised Garfinkle-Vachaspati Transform

Understand

The Garfinkle-Vachaspati transform is a deformation of a metric in terms of a null, hypersurface orthogonal, Killing vector $k^\mu$.

• We explore a generalisation of this deformation in type IIB supergravity taking motivation from certain studies of the D1-D5 system.
• We consider solutions of minimal six-dimensional supergravity admitting null Killing vector $k^\mu$ trivially lifted to type IIB supergravity by the addition of four-torus directions.
• The torus directions provide covariantly constant spacelike vectors $l^\mu$.