Wiener-Hopf factorisation, Toeplitz operators and the ergosphere of a rotating black hole

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• M. Cristina Câmara (University of Lisbon)
• Thursday 09 November 2023, 11:30-12:30
• External.

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BLHW02 - Machine learning toolkits and integrability techniques in gravity

Using a Riemann-Hilbert approach and the canonical Wiener-Hopf factorisation of certain matrix functions called monodromy matrices, one can obtain explicit solutions to the non-linear field equations of some gravitational theories. We address here, for the first time, the underlying question of what happens when a canonical factorisation does not exist and we use the close connection of Wiener-Hopf factorisation with Toeplitz operators to study this question. For the case of rational monodromy matrices, we prove that the non-existence of a canonical factorisation determines a curve in the Weyl coordinates plane where some elements of the metric tend to zero.  In the case of the Kerr black hole, it coincides with the ergosurface.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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