Abstract
We remind that the “ring down” features observed in the LIGO gravitational waves (GW) resulted from trembling of “photon spheres” (\(R_{\mathit{photon}}=3M\), by using units \(G=c=1\)) of newly formed compact objects and not from the trembling of their event horizons (EH) \(R=2M\) (Cardoso et al. 2016). Further, the tentative evidence for late time “echoes” in GWs might be signatures of horizonless compact objects rather than vacuum black holes (BHs) possessing EHs. In general, in the past, many authors have considered the possibility that the so-called BHs might be only BH mimickers (BHMs) having physical surfaces (\(R\approx 2M\)). Similarly, even for an ideal BH, the radius of its shadow, which is \(R_{\mathit{shadow}}=\sqrt{3}R_{\mathit{photon}}\), is actually the gravitationally lensed shadow of its photon sphere. Accordingly, any compact object having \(R\le R_{\mathit{photon}}=3M\) would generate similar shadow. Thus, no observation has ever detected any EH (any exact BH). Also, by definition, it is fundamentally impossible to directly detect any EH (Abramowicz et al. 2002). One notes that all astrophysical compact objects, except exact (chargeless) BHs, possess intrinsic magnetic moment that is dominated by the dipole component. Even rapidly spinning neutron stars (NS) are treated as spinning magnetic dipoles by ignoring the weak additional multipole moments. Hence, since an exact BH has no magnetic moment, a collapsing massive star must radiate away its multipole magnetic moments one by one and left with mostly the dipole moment immediately before becoming a BH (Ginzburg 1964). One also notes that the magnetic field embedded in the accreting plasma close to the compact object is expected to have a radial pattern of \(B\sim r^{-1}\), while the stronger BHM dipole magnetic field should fall off as \(B\sim r^{-3}\). 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 (Lobanov 2017). 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 \(\sim \frac{z_{s}}{\ln z_{s}}\), where \(z_{s}\gg 1\) is the surface gravitational redshift. We suggest that, by studying the radial variation as well as significant angular asymmetry of magnetic field structure near the compact object, future observations might differentiate a theoretical BH from a astrophysical BHM. 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.
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The Authors are thankful to the anonymous referee for his/her constructive critique and seeking clarification of many issues. We accordingly almost rewrote the manuscript and we believe this present version has much more scientific value than the original one.
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Mitra, A., Corda, C. & Mosquera Cuesta, H.J. How to distinguish an actual astrophysical magnetized black hole mimicker from a true (theoretical) black hole. Astrophys Space Sci 366, 25 (2021). https://doi.org/10.1007/s10509-020-03913-3
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DOI: https://doi.org/10.1007/s10509-020-03913-3