Black holes shielded by magnetic fields

Black holes (BHs) formed by collapsing and/or merging of magnetized progenitors, have magnetic fields penetrating the event horizon, and there are several possible scenarios. Thus, the no-hair theorem that assumes the outside medium is a vacuum, is not applicable in this case. Bearing this in mind and considering a Schwarzschild BH of mass M immersed in a uniform magnetic field B, we show that all three frequencies related to the equatorial circular orbit of a test particle become imaginary for the orbits of radii r_B>2B⁻¹. It signifies that if a BH is surrounded by a magnetic field of order B∼R_g⁻¹ (where R_g is the gravitational radius of the BH), a test particle could unable to continue its regular geodesic motion from/at r>r_B, hence the accretion disk could not be formed, and the motion of other stellar objects around the BH could be absent. As the BHs are generally detected by watching for their effects on nearby stars and gas, a magnetic field of order B∼R_g⁻¹ could be able to shield a BH in such a way that it could remain undetectable. Motivated with this theoretical investigation and considering the sphere (of radius r_f) of magnetic influence around an astrophysical BH, we constrain B, above which a magnetized BH could remain undetectable. For example, M=10⁹M_⊙ BH surrounded by B>10⁶ G and M=10M_⊙ BH surrounded by B>10¹⁴ G could remain undetectable for r_f∼10⁵R_g. In other words, our result also explains why a detected SMBH has surprisingly weak magnetic field.