https://neckpinch.com/authors/rashid-alawadhi/New arXiv papers by Rashid Alawadhi, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2305.18973/arxiv:2305.18973Tue, 30 May 2023 00:00:00 GMTRashid Alawadhi — This thesis applies the Kerr-Schild and the Weyl double copy formalisms to study various concepts in the physics literature. First we apply both the Kerr-Schild and the Weyl double copy to solution generating transformations in General Relativity, where we identify Ehlers transformation as the double copy of electromagnetic duality transformation. Secondly, as a spin-off of the Weyl double copy, we use gauge fields defined on curved spacetimes to construct the Weyl tensor and study a host of solution of Einstein's equations. This study provides a test of the non-triviality of the double copy formalism. The second half of the thesis deals with mathematical concepts of physical relevance. First we apply the Kerr-Schild double copy to the concept of holonomy groups of Riemannian manifolds. We find that the single copy of the Riemannian holonomy operator, which we dub SCH, to be a similar operator constructed from the single copy gauge-field curvature. This is followed by a study of this single copy operator on different solutions of Einstein equations and their respective single copies, where we find that the holonomy and SCH groups differ for the Taub-NUT metric, while both reducing to SU(2) for self-dual solutions. Lastly, we apply the Kerr-Schild double copy to the Ricci flow equation, interpreted as the beta function of the closed string, and obtain the Yang-Mills flow equation, which is physically interpreted as the beta function of the open string coupled to a gauge field.Ricci flowPhysics https://neckpinch.com/papers/2202.09874/arxiv:2202.09874Sun, 20 Feb 2022 00:00:00 GMTRashid Alawadhi — The perturbative double copy is by now a highly established correspondence between gravity and gauge theories. Non-perturbatively, information ranging from classical solutions to topological quantities on both sides have been related to each other via the double copy correspondence. In this paper, we add another result, where we show that the single copy of the Ricci flow is the Yang-Mills flow on the space of connections of a principal U(1)-bundle.Ricci flowPhysics