New gravitational solutions via a Riemann-Hilbert approach

Open Access
Regular Article - Theoretical Physics


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.


2D Gravity Black Holes Integrable Field Theories Sigma Models 


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© The Author(s) 2018

Authors and Affiliations

  1. 1.Center for Mathematical Analysis, Geometry and Dynamical Systems, Department of Mathematics, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  2. 2.Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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