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The photon surface is defined as a timelike surface $S$ such that any photonemitted in arbitrary tangential direction to $S$ from an arbitrary point on $S$continues to propagate on $S$. In this paper, we examine whether a staticphoton surface can be present in distorted electrovacuum spacetimes withperturbative approach, by constructing analytic solutions to the equations forstatic perturbations of a Reissner-Nordstr\"om spacetime that are regularoutside the background photon surface. For each of the $\ell\ge 2$ modes, thereare two physical solutions to the perturbative equations that correspond toadding the multipole moments of mass and electric charge, respectively. Byadjusting the ratio of the amplitudes of the two solutions appropriately, it ispossible to realize a distorted photon surface. In the case of $\ell=1$,although there is only one physical solution to the perturbative equations,there is also a degree of freedom to shift the coordinate position of thephoton surface, and this enables the formation of a photon surface. Such aphoton surface has a spherically symmetric spatial section, but it is alsodistorted in the three-dimensional sense. Our results show that distortedstatic photon surfaces can be formed at least at the level of the first-orderperturbations, and imply that the uniqueness of the photon surface may not holdin electrovacuum spacetimes.

Distorted static photon surfaces in perturbed Reissner-Nordstr\"om spacetimes