Meissner Effect in Kerr--Bertotti--Robinson Spacetime

We establish the black-hole Meissner effect for extremal Kerr--Bertotti--Robinson (Kerr--BR) black holes, which are exact solutions of the Einstein--Maxwell equations describing a rotating black hole immersed in a uniform Bertotti--Robinson electromagnetic universe. Using the near-horizon framework of Bi\v{c}\'ak and Hejda, we prove that for a purely magnetic external BR field the horizon-threading magnetic flux vanishes in the static limit of the near-horizon geometry, i.e.\ as the twist parameter $k\to 0$ when $Ba\to 1^-$, thereby establishing the Meissner effect analytically. The proof relies on two exact identities that hold at extremality for all values of the external field: $\Omega_x|_{r_e}=0$ and $\Omega_r|_{r_e}=B^2 a$, both consequences of the double-root structure of the horizon function $\Delta$. Together they force the azimuthal gauge potential $A_\phi|_{r_e}$ to become independent of the polar angle in the static limit, reducing to a pure-gauge constant on the horizon $S^2$ and expelling all magnetic flux. The Kerr--BR result is contrasted with the Kerr--Melvin family, where the static limit occurs at a finite interior field strength, and with the Melvin--Kerr--Newman--Taub--NUT spacetime, where the NUT parameter is known to prevent expulsion. An independent geometric argument based on the logarithmic divergence of the proper throat length corroborates the result, and its implications for Blandford--Znajek jet suppression near extremality are discussed.