Knotted solutions, from electromagnetism to fluid dynamics

• Published in: International journal of modern physics. A, Particles and fields, gravitation, cosmology Vol. 32; no. 33; p. 1750200
• Main Authors: Alves, Daniel W. F., Hoyos, Carlos, Nastase, Horatiu, Sonnenschein, Jacob
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 30.11.2017; World Scientific Publishing Co. Pte., Ltd
• Subjects: Couplings; Electromagnetism; Fluid dynamics; Mathematical analysis; Physics; String theory; knotted solutions; Classical field theory solutions; electromagnetism; fluid dynamics
• ISSN: 0217-751X; 1793-656X
• DOI: 10.1142/S0217751X17502001

Knotted solutions to electromagnetism and fluid dynamics are investigated, based on relations we find between the two subjects. We can write fluid dynamics in electromagnetism language, but only on an initial surface, or for linear perturbations, and we use this map to find knotted fluid solutions, as well as new electromagnetic solutions. We find that knotted solutions of Maxwell electromagnetism are also solutions of more general nonlinear theories, like Born–Infeld, and including ones which contain quantum corrections from couplings with other modes, like Euler–Heisenberg and string theory DBI. Null configurations in electromagnetism can be described as a null pressureless fluid, and from this map we can find null fluid knotted solutions. A type of nonrelativistic reduction of the relativistic fluid equations is described, which allows us to find also solutions of the (nonrelativistic) Euler’s equations.