How to distinguish an actual astrophysical magnetized black hole mimicker from a true (theoretical) black hole

Abstract

We remind that the ring down features observed in the LIGO GWs resulted from trembling of photon spheres (Rp=3M) of newly formed compact objects and not from the trembling of their event horizons (R=2M). Further, the tentative evidences for late time echoes in GWs might be signatures of horizonless compact objects rather than vacuum black holes (BHs). Similarly, even for an ideal BH, the radius of its shadow is R_shad = \sqrt{3}Rp is actually the gravitationally lensed shadow of its photon sphere. Accordingly any compact object having R \geq R = 3M would generate similar shadow. Thus, no observation has ever detected any event horizon or any exact BH. Also note that the magnetic field embedded in the accreting plasma close to the compact object is expected to have a radial pattern of B \sim 1/r while the stronger BHM dipole magnetic field should fall off as B \sim 1/r3. Accordingly it has been suggested that one may try to infer the true nature of the so-called astrophysical BHs by studying the radial pattern of the magnetic field in their vicinity. But here we highlight that close to the surface of BHMs, the magnetic field pattern differs significantly from the same for non-relativistic dipoles. In particular, we point out that for ultra-compact BHMs, the polar field is weaker than the equatorial field by an extremely large factor of \sim z_s/lnz_s, where z_s>>1 is the surface gravitational redshift. We suggest that by studying the of radial variation as well as significant angular asymmetry of magnetic field structure near the compact object, future observations might differentiate a theoretical black hole from a astrophysical BH mimicker. This study also shows that even if some BHMs would be hypothesized to possess magnetic fields even stronger than that of magnetars, in certain cases, they may effectively behave as atoll type neutron stars possessing extremely low magnetic fields.