A generalised Garfinkle–Vachaspati transform

• Published in: General relativity and gravitation Vol. 50; no. 12; pp. 1 - 40
• Main Authors: Mishra, Deepali, Srivastava, Yogesh K., Virmani, Amitabh
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2018; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Cosmology; Classical and Quantum Gravitation; Deformation; Differential Geometry; Gravity; Hyperspaces; Mathematical analysis; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Research Article; Spacetime; Supergravity; Supersymmetry; The Fuzzball Paradigm; Theoretical; Toruses; Vectors (mathematics); D1–D5 system; Fuzzball paradigm; Garfinkle–Vachaspati transform
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-018-2477-y

The Garfinkle–Vachaspati transform is a deformation of a metric in terms of a null, hypersurface orthogonal, Killing vector k μ . 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 μ trivially lifted to type IIB supergravity by the addition of four-torus directions. The torus directions provide covariantly constant spacelike vectors l μ . We show that the original solution can be deformed as g μ ν → g μ ν + 2 Φ k ( μ l ν ) , C μ ν → C μ ν - 2 Φ k [ μ l ν ] , provided the two-form supporting the original spacetime satisfies i k ( d C ) = - d k , and where Φ satisfies the equation of a minimal massless scalar field on the original spacetime. We show that the condition i k ( d C ) = - d k is satisfied by all supersymmetric solutions admitting null Killing vector. Hence all supersymmetric solutions of minimal six-dimensional supergravity can be deformed via this method. As an example of our approach, we work out the deformation on a class of D1–D5–P geometries with orbifolds. We show that the deformed spacetimes are smooth and identify their CFT description. Using Bena–Warner formalism, we also express the deformed solutions in other duality frames.