New gravitational solutions via a Riemann-Hilbert approach

TL;DR

This paper introduces a Riemann-Hilbert method for generating new solutions to gravity field equations by factorizing monodromy matrices, revealing solutions with novel and unusual properties.

Contribution

It develops a canonical factorization framework for non-meromorphic monodromy matrices in reduced gravity theories, enabling the construction of new solutions with unique features.

Findings

Established canonical factorization for a class of functions on spectral curves.

Applied factorization to deformed monodromy matrices to generate new solutions.

Discovered solutions with unusual properties not seen in previous models.

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.