Andreev reflection in Reissner–Nordström spacetime: coulombic pair-breaking and the electromagnetic Clogston radius

Phase-coherent transport across a normal-metal–superconductor (NS) junction outside a charged black hole (BH) turns curved-spacetime physics into a quantity an asymptotic observer reads from a current–voltage curve. The Schwarzschild case carries a single channel, the gravitational redshift of the gap, and it acts on the condensate only kinematically. Charging the BH opens a second channel with no Schwarzschild analogue. Across one BCS coherence length \(ξ \) the radial Coulomb field of the Reissner–Nordström geometry, which a static observer measures to be exactly \(Q/r²\) , shifts the electrochemical potentials of the two pair members by \(δ μ (r)=eQξ /r²\) , in analogy with the Zeeman splitting behind the Clogston–Chandrasekhar (CC) bound. Because this shift varies appreciably over one coherence length, the rigid-gap closure that carried the chargeless analysis fails, and the pair potential must be solved for as a function of position. Applied locally, the CC inequality then defines an electromagnetic Clogston (EMC) radius outside which pairing survives and inside which it collapses, and the gap profile across that radius is the domain wall joining the two degenerate phases. We solve the Bogoliubov–de Gennes (BdG) equations covariantly on the static slice and obtain a doubly modified Blonder–Tinkham–Klapwijk (BTK) conductance combining redshift-rescaling with Q -dependent erosion of the subgap plateau, together with a closed-form excess-current invariant. The extremal limit, treated intrinsically in the near-horizon AdS \(₂× S²\) throat, pushes the EMC radius outside the event horizon (EH) once \(Π >1/√2\) and yields a gapless conductance at infinity. Three suppression channels with distinct radial scalings separate kinematic redshift from local condensate response. Realistic charge-to-mass ratios place the mechanism far outside the reach of a charged neutron star, so the framework is offered as a controlled statement about fixed RN backgrounds and their holographic analogue rather than as an observational proposal.