The Fate of Black Hole-Induced Moduli Excursions in the Presence of Scalar Potentials

Large charged black holes can create macroscopic, locally weakly curved regions in which moduli take values different from their asymptotic values. We study how robust this mechanism is once the scalar has a nontrivial potential. In four-dimensional Einstein-Maxwell-dilaton theory, the massless GHS solution provides a finite exterior throat in which the scalar and the gauge coupling vary logarithmically. We develop fixed-throat diagnostics for the competition between the black hole gauge source and a scalar potential, and compare them with back-reacted exterior evolutions when needed. The relevant criterion is not the mere presence of a potential, but how its force behaves along the scalar trajectory traced by the black hole throat. Quadratic stabilizing potentials erase the throat when the Compton wavelength becomes comparable to the horizon scale. Runaway, periodic, and barrier-type potentials instead exhibit distinct failure modes controlled by their slope, sign, oscillations, or barrier distance along the GHS trajectory. A quintessence-like scalar remains effectively massless on astrophysical black hole scales, leaving the throat essentially unobstructed. If the charge belongs to a hidden sector, and if the scalar also controls visible couplings or bulk propagation, such surviving altered-modulus regions could leave phenomenological imprints in near-horizon accretion or emission.