Kerr-Bertotti-Robinson Spacetime and the Kerr/CFT Correspondence

We construct the Kerr/CFT correspondence for extremal Kerr–Bertotti–Robinson (Kerr–BR) black holes, which are exact stationary solutions of the Einstein–Maxwell equations describing a rotating black hole immersed in a uniform Bertotti–Robinson electromagnetic universe. After reviewing the geometry, horizon structure, and thermodynamics of the Kerr–BR family, we demonstrate that the external field non-trivially modifies both the horizon positions and the extremality condition. For extremal configurations, the near-horizon limit yields a warped ${\mathrm{A}\mathrm{d}\mathrm{S}}_3$ geometry with an associated Maxwell field aligned to the $U(1)$ fibration. Imposing standard Kerr/CFT boundary conditions, the asymptotic symmetry algebra gives rise to a Virasoro algebra with central charge $c_L$ and left-moving temperature $T_L$ that depend explicitly on the external field strength. The Cardy formula then reproduces exactly the Bekenstein–Hawking entropy of the extremal Kerr–BR black hole for any admissible value of the Bertotti–Robinson field, thereby establishing a consistent Kerr/CFT dual description. Comparisons with the magnetized Melvin–Kerr and Kaluza–Klein black holes are briefly discussed, highlighting qualitative differences in their curvature profiles and horizon geometries.