PT and anti-PT symmetries for astrophysical waves

Astronomy & Astrophysics manuscript no. PTsym_in_astro ©ESO 2024
May 30, 2024
PT and anti-PT symmetries for astrophysical waves
Armand Leclerc1,⋆, Guillaume Laibe1, and Nicolas Perez1
Univ Lyon, Univ Lyon1, Ens de Lyon
CNRS, Centre de Recherche Astrophysique de Lyon UMR5574
F-69230, Saint-Genis-Laval, France
Received September 15, 1996; accepted March 16, 1997

ABSTRACT
Context. Discrete symmetries have found numerous applications in photonics and quantum mechanics, but remain little studied in fluid mechanics, particularly in astrophysics.
Aims. We aim to show how PT and anti-PT symmetries determine the behavior of linear perturbations in a wide class of astrophysical problems. They determine the location of exceptional points in parameter space and the associated transitions to instability, and are associated with the conservation of quadratic quantities that can be determined explicitly. Methods. We study several classical local problems: the gravitational instability of isothermal spheres and thin disks, the Schwarzschild instability, the Rayleigh–Bénard instability, and acoustic waves in dust–gas mixtures. We calculate the locations and the order of the Exceptional Points using a method of resultants, as well as the conserved quantities in the different regions of the parameter space using Krein theory. Results. All problems studied here exhibit discrete symmetries, even though Hermiticity is broken by different physical processes
(self-gravity, buoyancy, diffusion, drag). This analysis provides genuine explanations for certain instabilities, and for the existence of regions in the parameter space where waves do not propagate. These correspond to the breaking of PT and anti-PT symmetries, respectively. Not all instabilities are associated with symmetry breaking (e.g., the Rayleigh–Benard instability).
https://arxiv.org/pdf/2405.18901