Stealth black hole solutions in higher-order Maxwell–Einstein theories

In this paper, we study static and spherically symmetric black hole solutions in higher-order Maxwell–Einstein theories. We do not particularly focus on the degenerate classes of theories. For several specific choices of the coupling functions, we show that in the presence of the ordinary Maxwell kinetic term, the Reissner–Nordström–(anti-)de Sitter solution in the pure Maxwell–Einstein theory can also be a solution in generic classes of higher-order Maxwell–Einstein theories, and in the absence of the ordinary Maxwell kinetic term, the Schwarzschild–(anti-)de Sitter solution with the nonzero electric field can be obtained. This corresponds to a stealth black hole solution as the electric field does not affect the spacetime geometry. We then focus on several degenerate classes of higher-order Maxwell–Einstein theories, and find that the dyonic Reissner–Nordström–(anti-)de Sitter solution in the pure Maxwell–Einstein theory can be a solution.