On relativistic gasdynamics: invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections. (25th November 2020)

• Record Type: Journal Article
• Authors: Rogers, C.; Ruggeri, T.; Schief, W. K.
• Is Part Of: Proceedings. Volume 476:Number 2243(2020)
• Publication Date: 2020-11-25
• Subjects: relativistic -- gasdynamics -- reciprocal -- invariance -- Heisenberg spin; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2020.0487
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-parameter class of reciprocal transformations. The class of invariant transformations originally obtained by Bateman in non-relativistic gasdynamics in connection with lift and drag phenomena is retrieved as a reduction in the classical limit. In the general 3+1-dimensional case, it is demonstrated that Synge's geometric characterization of the pressure being constant along streamlines encapsulates a three-dimensional extension of an integrable Heisenberg spin equation.