This paper studies when a charged black hole placed inside a Bertotti–Robinson universe preserves supersymmetry in a specific four-dimensional supergravity theory (N=2, D=4). The Bertotti–Robinson spacetime is the product AdS2 × S2 and is the familiar near‑horizon limit of an extremal Reissner–Nordström black hole. Supersymmetric backgrounds are singled out by the existence of nontrivial solutions of the Killing spinor equations—spinor fields that represent unbroken supersymmetry. Such solutions are interesting because they are often stable and easier to study in quantum gravity settings.

The authors start from a family of exact solutions found by Ovcharenko and Podolský that describe possibly accelerating, charged black holes immersed in a Bertotti–Robinson electromagnetic background. The family depends on a few parameters: B (the Bertotti–Robinson electromagnetic strength), w (a charge duality parameter: w=1 is purely electric, w=0 purely magnetic), α (an acceleration parameter), and m (related to the black hole mass). There are two discrete branches of the general solution. The branch with r0≠0 contains the charged, possibly accelerating Reissner–Nordström black hole in the Bertotti–Robinson universe; the other branch contains uncharged cases.

Focusing on the charged branch, the authors examine the Killing spinor equations of N=2, D=4 gauged supergravity and solve them explicitly. They find that the only new supersymmetric subcase in this family is the extremal Reissner–Nordström black hole sitting in the Bertotti–Robinson background. In the extremal limit (obtained by a specific redefinition of parameters and taking α→B) the radial function controlling horizons becomes a perfect square, ∆r=(r−m)^2, and the solution has no acceleration horizon or conical axis singularities. When B=0 this reduces to the usual extremal Reissner–Nordström black hole; when m=0 it reduces to the Bertotti–Robinson universe written in accelerating coordinates.