Geometry-induced exceptional rings in a non-Hermitian Dirac model on a cosmic string background

We formulate a non-Hermitian extension of the Dirac equation in the conical spacetime of a cosmic string by introducing a non-PT-symmetric scalar interaction. We show that the competition between topology and complex deformation induces a nontrivial spectral structure with geometry-controlled shifts and a radial gain/loss profile. A central result is the emergence of a spatially localized exceptional ring at a finite radius, generated by the competition between conical geometry and non-Hermitian effects. In contrast to conventional exceptional points in parameter space, this structure is intrinsically realized in real space and marks a transition between distinct dynamical regimes. The radial Dirac system is shown to admit an exact decoupling into Schrödinger type equations associated with biconfluent Heun structures. These results establish a direct link between spacetime topology and non-Hermitian spectral properties.