New gravitational solutions via a Riemann-Hilbert approach

Abstract

We consider the Riemann-Hilbert factorization approach to solving the field equations of dimensionally reduced gravity theories. First we prove that functions belonging to a certain class possess a canonical factorization due to properties of the underlying spectral curve. Then we use this result, together with appropriate matricial decompositions, to study the canonical factorization of non-meromorphic monodromy matrices that describe deformations of seed monodromy matrices associated with known solutions. This results in new solutions, with unusual features, to the field equations.

29 pages, 2 figures; v2: reference added, matches published version

References in corpus (5)

• Statistical Description of Rotating Kaluza-Klein Black Holes
• Infinite-Dimensional Symmetries of Two-Dimensional Coset Models Coupled to Gravity
• An Inverse Scattering Construction of the JMaRT Fuzzball
• Geroch Group Description of Black Holes
• A Riemann-Hilbert approach to rotating attractors

Cited by in corpus (6)

• Weyl metrics and Wiener-Hopf factorization
• Geroch Group Description of Bubbling Geometries
• Riemann-Hilbert problems, Toeplitz operators and ergosurfaces
• Generating new gravitational solutions by matrix multiplication
• Classical integrability in the presence of a cosmological constant: analytic and machine learning results
• Solving gravitational field equations by Wiener-Hopf matrix factorisation, and beyond