A Riemann-Hilbert approach to rotating attractors

Abstract

We construct rotating extremal black hole and attractor solutions in gravity theories by solving a Riemann-Hilbert problem associated with the Breitenlohner-Maison linear system. By employing a vectorial Riemann-Hilbert factorization method we explicitly factorize the corresponding monodromy matrices, which have second order poles in the spectral parameter. In the underrotating case we identify elements of the Geroch group which implement Harrison-type transformations which map the attractor geometries to interpolating rotating black hole solutions. The factorization method we use yields an explicit solution to the linear system, from which we do not only obtain the spacetime solution, but also an explicit expression for the master potential encoding the potentials of the infinitely many conserved currents which make this sector of gravity integrable.

arXiv commentMinor changes, final version, accepted by JHEP. 75 pages, 2 figures

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Cited by in corpus (9)

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• 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