Haryanto Mangaratua Siahaan

We study the black-hole Meissner effect for extremal Kerr–Bertotti–Robinson (Kerr–BR) black holes, exact Einstein–Maxwell solutions describing a rotating black hole immersed in a uniform Bertotti–Robinson electromagnetic universe. We show that extremality alone is not sufficient for complete magnetic-flux expulsion in this family. For a purely magnetic external BR field, finite extremal holes with $$0<Ba<1$$ 0 < B a < 1 carry the exact northern-hemisphere flux $$\Phi _N=-2\pi Ba^2\sqrt{1-B^2a^2}$$ Φ N = - 2 π B a 2 1 - B 2 a 2 , which is nonzero and maximal in magnitude at $$Ba=1/\sqrt{2}$$ B a = 1 / 2 . Complete expulsion occurs only in the static near-horizon boundary limit $$Ba\rightarrow 1^-$$ B a → 1 - , equivalently $$k\rightarrow 0$$ k → 0 , where the U (1) fibration of the near-horizon metric trivialises. The proof relies on two exact identities that hold at extremality for all values of the external field, $$\Omega _x|_{r_e}=0$$ Ω x | r e = 0 and $$\Omega _r|_{r_e}=B^2a$$ Ω r | r e = B 2 a , both consequences of the double-root structure of the horizon function $$\Delta $$ Δ . Together they force the azimuthal potential $$A_\phi |_{r_e}$$ A ϕ | r e in the purely magnetic sector to become independent of the polar angle in the static boundary limit, so that the gauge-invariant horizon flux density $$F_{x\phi }|_{r_e}$$ F x ϕ | r e and the flux through any smooth horizon cap vanish. 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. A complementary throat-geometry argument and qualitative implications for Blandford–Znajek jet suppression near the static boundary of the extremal branch are discussed.

We study black-hole shadows in a magnetized Kaluza--Klein rotating dilaton spacetime equipped with a NUT charge. We show that the null Hamilton--Jacobi equation remains separable after magnetization: the Kaluza--Klein embedding preserves a rank-2 conformal Killing--St\"ackel tensor, which yields compact one-dimensional potentials \(R(r)\) and \(\Theta(\theta)\) and a Carter-like constant. This behavior is in contrast with Ernst-magnetized solutions in pure Einstein--Maxwell theory, where separability is typically lost. Taking advantage of integrability, we derive analytic conditions for spherical photon orbits, construct the observer screen map, and evaluate the Hioki--Maeda observables \(R_s\) (reference--circle radius) and \(\delta_s\) (distortion). We establish the separability directly from the frame structure of the magnetization, and show that the relevant hidden symmetry is a genuine Killing tensor of the conformally rescaled metric \(g_{\mu\nu}/(\Sigma\chi)\). We show that the local removability of the Manko--Ruiz parameter \(C\) known for Kerr--Taub--NUT remains valid in the unmagnetized limit, whereas magnetization renders configurations with different \(C\) non--isometric and induces a \(C\)--dependence of the shadow with quadratic onset, and that the equatorial surface ceases to be a generically invariant photon plane when the NUT charge is nonzero. The framework reduces to the unmagnetized Kerr--Taub--NUT seed as \(b\!\to\!0\) and to Kerr as \(b\!\to\!0\) and \(\ell\!\to\!0\). The finite--observer shadow construction is validated against the closed--form Kerr--Taub--NUT boundary of Grenzebach, Perlick and L\"ammerzahl to machine precision, with the quantitative shadow analysis limited to an equatorial observer. We evaluate the astrophysical magnitude of the effect and find \(bM\sim10^{-9}\) for M87\(^{\ast}\), so that the results are of structural rather than observational significance.

We construct an exact magnetized generalization of the Zipoy-Voorhees spacetime by applying the magnetic Harrison transformation to a static seed with quadrupolar deformation parameter $k$. The resulting Melvin-Zipoy-Voorhees metric is a solution to the Einstein-Maxwell equations that interpolates between the unmagnetized Zipoy-Voorhees geometry and the Melvin magnetic universe. We analyze the algebraic structure, finding the spacetime to be generically of Petrov type I, and investigate the equatorial dynamics of charged test particles and photons. Our analysis reveals that the external magnetic field $b$ induces a ``Lorentz shift'' in the effective angular momentum, suppressing the potential barrier and causing the Innermost Stable Circular Orbit (ISCO) to migrate inward. In contrast, the radius of the photon ring shifts slightly outward with increasing magnetization.

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 $\mathrm{AdS}_3$ 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.