Analytic study on backreacting holographic superconductors with dark matter sector

Abstract

The variational method for the Sturm-Liouville eigenvalue problem is employed to study analytically properties of the holographic superconductor with a dark matter sector, in which a coupling between the Maxwell field and another $U(1)$-gauge field is considered. The backreaction of the dark matter sector on the gravitational background in question is also examined.