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

The tentative evidences for late time"echoes"in LIGO gravitational waves (GWs) have been claimed to be signatures of horizonless compact objects rather than vacuum black holes (BHs) possessing horizons. In general, in the past, many authors have considered the possibility that the so-called BHs might be only BH mimickers (BHMs). And recently it has been suggested that the true astrophysical BH having no intrinsic magnetic fields may be differentiated from magnetized BHMs by studying the radial variations of magnetic fields around pertinent compact objects (Lobanov, Nat. Astron. 2017). Here we highlight that close to the surface of BHMs, the magnetic field pattern differs significantly from the same for non-relativistic Neutron Stars (B\sim r^{-3}). 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}\gg1 is the surface gravitational redshift. We suggest that by studying the of radial variation as well as such significant asymmetry of magnetic field structure near the compact object, future observations may differentiate a theoretical black hole from a astrophysical BH mimicker (a compact object). 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.


Introduction
While most of the astronomers believe that the astrophysical BH candidates (BHCs) found in innumerable X-ray binaries and Active Galactic Nuclei are true mathematical BHs possessing event horizons and singularities, from time to time, in order to avoid many puzzles and paradoxes with BH singularities and event horizons, many general relativists and astrophysicists have suggested that such objects could be BHMs, which are almost as compact as BH (R ≈ R s = 2M ) but non-singular and without exact event horizons. Here R and R s represent the (areal) radius of the compact object and Schwarzschild radius respectively (units with G = c = 1 will be used in this paper). Technically, one basic difference between a true BH and a BHM can be expressed through the concept of gravitational redshift around compact object: and on the surface of the compact object: For a mathematical true BH, one must have z s = ∞ while for a BHM, thoughz s is finite though it can be arbitrarily high: 1 ≪ z s < ∞.
Such ideas have been boosted by tentative evidences for late time "echoes" following the "ring down" phases of several LIGO GW emitters [1,2]. On the other hand, it is a general conviction that at least one among the various LIGO detections, i.e. the event GW170817, represents a GWs detection from a neutron star merger rather than a BH merger [3]. In the case of a horizonless compact object formed by the merger of two smaller compact objects, GWs trapped within the compact object can leak out of its surface after repeated trials. Such repeated (partial) reflections or internal barrier penetrations from the compact object may give rise to GW "echoes" following the initial ring down phase. It is important to recall that, though originally the "ring down" phase was considered as evidence for Event Horizons (R = R s ) of the compact objects formed from the merger two smaller compact objects (BHs or neutron stars), it turned out that, ring down may result from vibrations of photon ring, whenever there is enough energy trapped therein (r = 1.5R s = 3M ) or a bit outward, from the perturbed gravitational field itself, around horizonless compact objects (R ≥ 2M ) as well.
Naturally, if the claimed evidences for the late time GW echoes are genuine, we already have observational evidence that the so-called BHCs are horizonless BHMs. An important issue is that such an eventual confirmation will point out the end of general relativity as the correct theory for gravity, as gravitational waves overtones are not allowed by general relativity, and eventually such a signature may enlighten one right into the direction to build up a consistent quantum theory of gravitation.
On the other hand, it will be prudent to explore presence or absence of horizons in the BHCs from other astrophysical considerations. At first sight, one may think that the Event Horizon Telescope (EHT) may be able to image the event horizon of Sgr A * , the supermassive BH candidate at the centre of our galaxy [4]. But by definition, event horizon (r = R s ) cannot be directly imaged [5], and one can at the most image the close vicinity of a BH (r R s ) by means of the electromagnetic emission emanating thereof [4]. Hence even EHT may not be able to differentiate a BH from a BHM [6], with an important exception. In fact, the EHT with its present technology could find a signature of an actual astrophysical magnetized BHM. In especial, this goal can be realized if the effects predicted by nonlinear electrodynamics (NLED) associated to the gravitational redshift [36], as well as those related to the Doppler shift of encircling material around a BH, are called for in the characterization of such an astrophysical magnetized compact star mimicking a BH (see discussion below). For instance, it was very, very recently discovered by a Hubble Space Telescope (HST) Team [44] that the low-luminosity galaxy NGC 3147 (~130 million light-years away), which is of the sort of those that are normally thought to contain insufficient matter to support a disk of material being sucked into the BHs at their center, possesses at its center some compact object (say, a BH, if one prefers, which has a mass~250 million solar masses), around which it was found an extremely thin accretion disk. In fact, the disk of material is deeply embedded in the intensely powerful gravitational field of the BH, to the extent that light emanating from it is significantly distorted. However, the disk that the NASA/ESA HST astronomers observed resembles those commonly seen in much larger and more (luminous) active galaxies.
The attentive reader is also invited to think about the following arguments in [44]: • BHs in certain types of galaxies such as NGC 3147 are considered to be starving as there is insufficient gravitationally captured material to feed them regularly. It is therefore puzzling that there is a thin disk encircling a starving BH that mimics the much larger disks found in extremely active galaxies.
• Indeed, according to [44] "It is the same type of disk we usually see in objects that are 1,000 or even 100,000 times more luminous than NGC 3147".
• The surprise is that the authors of [44] thought the BH was so malnourished, it shouldn't have such a structure around it. It's basically a "Mini-Me" version of more powerful disks seen in very active galaxies. Besides, "The predictions of current models for very faint active galaxies clearly failed" [44].
• The team analyzed data collected by HST from the BH in question finding that the disk of material surrounding it was spinning at around 10 percent the speed of light, thus, "The type of disk we see is a scaled-down quasar that we did not expect to exist" [44].
• At such extreme velocities, the gas appears to brighten as it travels toward Earth on one side, and dims as it speeds away from our planet on the other. This effect is known as relativistic beaming. "This is an intriguing peek at a disk very close to a BH, so close that the velocities and the intensity of the gravitational pull are affecting how the photons of light look" [44].
• BHs in certain types of galaxies like NGC 3147 are malnourished because there is not enough gravitationally captured material to feed them regularly. So, the thin haze of infalling material puffs up like a donut rather than flattening out in a pancake-shaped disk. Therefore, it is very puzzling why there is a thin disk encircling a starving BH in NGC 3147 that mimics much more powerful disks found in extremely active galaxies with engorged, monster BHs.
• Thus, the next step is to search for other disks surrounding black holes in similar low luminosity galaxies to NGC 3147.
Such structure was said to be "anomalous" because the purported BH is observed as a very active one encircled by a thin accretion disk, and whose luminosity resembles one of the most typical AGN whose luminosity is about 1000 -1000.000 times the one in NGC 3147. At this point, recall that what current observations of active galactic nuclei (AGN) suggest is that their accretion disk structure is such that at the outermost side its radius gets close to R out = 2000 R g , while their innermost radii get around 10 − 100 R g . (NGC 3147 actual inner radius R inner ∼ 77±15 R g ). And in the specific case of AGN dominated by Bardeen-Petterson effect [45], the innermost accretion disk radius is located at about R BP ∼ 10 R g ! Then, if one assumes that the magnetic field strength at the outermost radius is estimated to be B out ∼ 10 4 Gauss, it follows that the amplification of the field strength for an observer at R A.H. ∼ 5R g gets close to [47] B out ∼ 8 × 10 11 R out Gauss.
This value of the strong magnetic field governs the relation describing relativistic effects on the radius of the compact object in the Born-Infeld NLED framework [47] (we consider the case where g rr = r 2 ...) where b = 9.8×10 15 e.s.u. arises from the Born-Infeld NLED Lagrangian, see [47] for details. Although when looking deep into the gravitational field of massive and supermassive BHs the NLED effect is not so easy to disentangle, the present calculation suggests that the same effect can clearly be checked for through observations of stellar-mass compact objects such neutron stars, and the like, where B-fields around 10 14−15 Gauss are well known to exist at radius R A.Disk ∼ 10−100 R N S . It is just to figure out what would appear as the actual gravitational redshift if one could look deep into as close as to the neutron star actual surface.
Meanwhile, knowing that the EHT Collaboration can look, with high resolution, inside the structure around an extremely compact object as close as 5 R g , it comes out that attempting to measuring simultaneously both the NLED gravitational redshift and the Doppler shift of absorption lines at such a radius of an AGN may disentangle the nature of the astrophysical magnetized compact object hidden inside the nucleus of an active galaxy: Is it a true BH or an actual magnetized BHM? This way, the EHT collaboration could indeed test for the NLED effects on the dynamics of systems like NGC 3147, or those of its sort.
Way back in 1964, Ginzburg pointed out that the collapsing massive star having frozen in magnetic field should develop strong dipole magnetic field immediately before becoming a BH, and in fact it may end up an ultra-magnetized "superstar" [7]. In addition, Thorne showed back in 1965 that pure magnetic energy would not collapse into a BH state [8]. It may be that there are stable gravitationally compact objects that are composed of relatively cool matter and magnetic fields without horizon and singularities. Despite such a theoretical vacuum, ever since then, innumerable authors, including Ginzburg himself, have considered the possibility that the compact objects at the core of the quasars could be spinning ultra-magnetized superstars, something like giant pulsars [9 -25]. In particular, Ginzburg and Ozernoi [13] coined a term "Magnetoids" to describe such spinning magnetized supermassive stars, supported by em radiation pressure, magnetic field and centrifugal repulsion. Several years before this, Morrison [9] proposed that both pulsars and quasars comprise em central, magnetized, spinning, condensed mass. The precursor to such works was the the idea of "supermassive" stars, supported purely by radiation pressure, by Hoyle and Fowler [26]. Such ideas however never discussed why a massive collapsing gas cloud must attain its Eddington Luminosity to become a non-singular Radiation Pressure Supported Star (RPSS) instead of inexorably collapsing all the way to become a singular BH.
This theoretical vacuum was filled in 2000-2, and a much more solid case was made for existence of quasi-static ultra-magnetic compact objects Mag-netospheric Eternally Collapsing Objects (MECOs) [27,28]. The physics of formation of MECOs were clarified later. It turned out that MECOs are essesntially extremely general relativistic versions of Radiation Pressure Supported Stars whose concept was originally given by Hoyle and Fowler [26]. Radiation Pressure Supported stars are so hot that they are radiating at their Eddington Limit where, by definition, the outward radiation pressure balances the inward gravitational pull. The concept of a MECO relies on the fact that during continued collapse, the outward force due to trapped radiation increases much faster ∼ (1 + z s ) 2 , than the relevant Eddington luminosity ∼ (1 + z s ). Consequently, at some approriately high z s ≫ 1, there should a quasi-equilibrium upon attainment of Eddington luminosity by the collapsing object [29 -34]. While most of the BHMs rely on general relativity or quantum gravity, one suggestion has been based on nonlinear electrodynamics (NLED) [35]. The idea in [35] was to use a particular NLED Lagrangian to address the BHMs issue. Such a Lagrangian was previously used in various analyses in astrophysics, like surface of neutron stars [36] and pulsars [37] and also on cosmological contexts [38]. In fact, it has been carefully explained in [36] and [37] that the effects arising from a NLED become quite important in super-strongly magnetized compact objects, such as pulsars, and particular neutron stars. Some examples include the so-called magnetars and strange quark magnetars. In particular, NLED modifies in a fundamental basis the concept of gravitational redshift as compared to the wellestablished method introduced by standard general relativity [36]. The analysis in [36] proved that unlike general relativity, where the gravitational redshift is independent of any background magnetic field, when a NLED is incorporated into the photon dynamics, an effective gravitational redshift appears, which happens to depend decidedly on the magnetic field pervading the pulsar. An analogous result has also been obtained in [37] for magnetars and strange quark magnetars. The resulting gravitational redshift tends to infinity as the magnetic field grows larger [36,37], as opposed to the predictions of standard general relativity. Thus, it is important to stress that the gravitational redshift of neutron stars is connected to the mass-radius relation of the object [36,37]. As a consequence, NLED effects turn out to be important as regard to the mass-radius relation, and one can also reasonably expect important effects in the case of BHCs where the mass-radius ratio is even more important than for a neutron star [35].
Traditionally, the primary means to study BHCs has been the X-ray and Radio studies of the accretion process around them when they are present in close X-ray binaries or in Active Galactic Nuclei having accretion disks. And there could indeed be a unique window to differentiate a true BH with a BHM in case the latter will be magnetized. This is so because, the non-charged Schwarzschild or Kerr black holes do not possess any intrinsic magnetic field. The accretion disk and accretion flow around them of course can generate magnetic field surrouding them. In order to appreciate this line of thinking, let us recall the case of accreting neutron stars having intrinsic magnetic fields. The accretion process generates secondary ambient magnetic field around the compact object. But in the vicinity of an accreting neutron star, the accretion generated magnetic field is usually much weaker than the primary neutron star magnetic field; and the former is thus ignored in the region away from the accretion disk. In particular, the region inside the magnetosphere bounded by the Alfvén surface [39] is completely dominated by the intrinsic magnetic field of the neutron star. The question of relative strengths of primary and secondary magnetic fields apart, the basic pattern of these components of magnetic field is different. It has been tentatively predicted that the secondary accretion origin magnetic field may vary as ∼ r −1 . In contrast, the primary intrinsic magnetic field of strongly magnetized BHMs may fall of as ∼ r −3 [6].
In 2002-3, Robertson and Leiter claimed that the extremely low quiescent X-ray flux of several Low Mass X-ray Binaries (LMXBs) containing BHCs could be explained by assuming that the so-called BHCs are actually ultra-magnetized spinning BHMs [40,41]. In addition, they pointed out that the quiescent weak X-ray flux from several LMXBs containing weakly magnetized spinning neutron stars too can be explained the ascribing the quiescent emission to the spin down luminosities [42].
But one may wonder how can one put spinning ultra-magnetized BHCs and weakly magnetized neutron stars on the same platform? We shall probe this question in the following. And, more generally, we shall highlight that in the close vicinity of the compact object, the radial variation of the magnetic fields for a BHM and secondary accretion generated magnetic field for a BH are far more complicated than a simple ∼ r −3 and ∼ r −1 patterns.
It is important to note that the present discussion is not unique to MECOs, and on the other hand, equally valid for any magnetized BHM.

General Relativistic Magnetic Dipole
Objects having such superstrong fields will certainly have higher order multimomets. However, since by the no-hair theorem [43] BHs can only have charge, all higher order electromagnetic moments must be radiated away before the formation of the event horizon [7]. In fact, eventually, even the dipole moment must be supressed [7]. As a consequence, charge neutral BHMs are expected to dominated only dipole moments. Even for neutron stars which are almost non-relativistic objects, the leading magnetic moment is the dipole one. It is well known that the dipole magnetic field has significant angular asymmetry, see ref. [46] on group on general relativistic effects of strong magnetic fields, in which an important geometric factor appears affecting the spatial distribution of the B-field.
For a non-relativistic neutron star (NS), the polar and radial components of the dipole field are and where µ is the magnetic dipole moment (as seen by a distant observer) and 4πr 2 denotes invariant area of symmetric 2-spheres. Here B θ and B r are the components of the magnetic field in local tetrad and B = B θ 2 + B r 2 . Thus, the magnetic field strength at the pole is twice the equatorial field: Given such an asymmetry at the non-relativistic level, one might expect that, for a general relativistic compact object, B p should be larger than B e by a factor larger than 2.0. It is needed to compare it to calculation of B-field (angular and radial) components in general relativity, (see ref. [46] on general relativistic effects of strong magnetic fields, in which an important geometric factor appears affectinf the spatial distribution of the B-field). However, here we point a previously unnoticed general relativistic effect: for a sufficiently relativistic compact object, the polar magnetic field becomes weaker than the equatorial field in direct contrast to their corresponding Newtonian behaviour. The same general relativistic effect has been computed in [46] for hyper-magnetized neutron stars, where such an effect clearly shows up.
At the outset of this study, we recall that the compactness of a relativistic object may be expressed in terms of its surface gravitational redsfift.
For an ideal NS having M = 1.44M ⊙ , and R = 10 km, it follows that z s ≈ 0.15, where M ⊙ stands for solar mass. In extreme contrast, for a Schwarzschild BH event horizon, by definition, one finds z s = ∞. Thus any proposed BHM must possess z s ≫ 1.
Given the fact that the polar fields of neutron stars are 100% stronger than the equalorial fields, one might think that BHMs should behave like supermagnetars whose polar fields are much stronger than the corresponding equatorial values. But in the following, we show that, the polar fields of BHMs could be weaker than the equatorial fields by million times or even larger. Yet eventually BHMs may even behave like low magnetic field millisecond pulsars or atoll type neutron stars in X-ray binaries.

General Relativistic Dipole Magnetic Field
The general relativistic modification of assumed dipole magnetic fields are known for many decades [7,48]. The components of field in local tetrads are: where x = r/2M and One easily sees that and, for z ≫ 1, we have Then, one sees from equations (11) and (12) that, in this limit, one gets ne also notes that since the RHS of equation (15) is dominated by the 3/ √ ǫ, term while the same for equation (16) is dominated by the ln z term if one would consider a range of z s > 10 5 . While such a large value of z s could be surprising, recall that for a true BH z s = ∞ and that any finite number is infinitely smaller than ∞! So for such extremely relativistic BHMs, in the immediate vicinity, one has Such analytical estimates have been verified by means of simple numerical evaluations too: Surf ace redshif t z s 10 10 10 8 10 6 Consequently, the magnetic fields at the equator and pole of the BHM are respectively: Thus, Accordingly, for a BHM with z s = 10 10 , one should expect Hence, even if one hypothesizes that the equatorial field of a stellar mass BHM is even stronger than that of magnetars, sayB e 10 16 G, the polar field could be very weak: B p ∼ 10 8 . One notes that, for x ≫ 1, both F 1 , F 2 ∼ 1 and the dipole field approaches non-relativistic form: In any case, there will be an ambiguity about the evaluation of local magnetic moment at the surface of the BHM. To some extent, such an ambiguity exists even for the non-relativistic case too.

Discussions
The massive compact objects found at the centre of most of the galaxies and in many X-ray binaries are certainly not neutron stars. In fact, neutron stars cannot be more massive than three solar massess. And such compact objects are believed to be BHCs. Despite this, in the past two decades, many authors have suggested various alternatives to true BHs and which may generically be termed as BHMs. And, in any case, independently of such suggestions, it is important to confirm that BHCs are indeed vacuum BHs possessing event horizons. One of the best attempts to ascertain the BHC at the centre of our galaxy will be imaging it by the EHT. However, even for an isolated ideal mathematical BH, the image will be characterized by unknown spin and the unknown orientation of the spin axis with the line of sight [4]. In addition, the image will be distorted and inflated by the strong gravitational lensing around the compact object. In practical cases, the presence of accretion disk having unknown geometry, accretion flow and radiation from the same will significantly modify the resultant image. In fact, the image of the supposed BHC can only be due to emission from the surrounding plasma and not from the "event horizon" from which no radiation can emerge [4]. Thus, in reality, even the EHT cannot distinguish a true BH possessing an event horizon (R = 2M ) from a BHM having R ≈ 2M . Accordingly, it has been suggested that, one may attempt to do this by studying the magnetic fields around BHCs [6].
In fact, in view of many similarities between X-ray binaries having old relatively weaker magnetic fields and BHCs, Robertson and Leiter [40 -42] wanted to study them on a common platform by assuming the BHCs are actually magnetized BHMs. They presented tentative evidence that the power-law part of the quiescent X-ray emissions of neutron stars in low-mass X-ray binaries is magnetospheric in origin [40]. Additionally, their work strongly suggested that the spectral state transition to the low hard state for neutron stars is a magnetospheric propeller effect [41]. They found that while NSs would require µ ∼ 10 27 G cm 3 , the BHCs would require intrinsic magnetic moments µ ∼ 10 29−30 G cm 3 for explaining their quiescent emissions as well as state transitions in this unified model. Such ideas are due to the fact they could explain the observed correlations between X-ray and radio luminosities found in BH as well as NS x-ray binaries in the same framework [41]. Further, there have been indirect evidences that the BHCs in the most of the quasars too possess strong intrinsic magnetic fields [49 -51].
In addition, it has been recently suggested that one should use the magnetic field pattern around accreting compact objects to test whether they are true BHCs or not. While uncharged BHs possessing event horizons do not possess any magnetic field, the plasma accreting onto them can possess magnetic field and which may vary as ∼ r −1 [6]. In contrast, even uncharged BHMs may possess own magnetic fields, and in particular, MECOs should possess strong intrinsic magnetic fields. At first sight, the magnetic field around a magnetized BHM should be dominated by the intrinsic dipole field falling off as r −3 because the ma netic field in the plasma (∼ r −1 ) is expected to be much weaker to the intrinsic field of the BHM [6].
Here we highlight the fact that, in the immediate vicinity of the BHM, the field pattern should be much complex than that of a neutron star: B ∼ r −3 . This is because while the radial field B r ∼ 3 µ R 3 z s , the polar field B p ∼ 12 µ R 3 ln z s . Thus, on the surface of the BHM, the magnetic field at the pole (B p ) is weaker than the same at equator (B e ) by an extremely large factor of ∼ z s /lnz s . And therefore, even an ultramagnetized BHM may behave as a neutron star whose magnetic field could be weaker than the same of young neutron stars by a factor of order 10 4 . And this realization gives us a clue as to why the previous attempts to study BHCs as magnetized BHMs may be qualitatively correct. Now, let us study the behaviour of the expected magnetic moments by neglecting the trigonomentric factors: For a moment, let us consider a BHC having M = 10M ⊙ and R = 3.10 6 cm (z s ≫ 1). The magnetic moment measured locally on the surface of this BHMs µ R ∼ 2.7.10 19 B G cm 3 . For a perfect axisymmetric case, the observed magnetic moment may be determined by B r . Hence, for such a case, even the local value µ R ∼ 2.7 10 19 B p could indeed be ∼ 10 27 G cm 3 or even much lower. However, for a non-aligned rotator B θ will play its role and one should have µ R ≫ 10 29 G cm 3 . But it is important here to note that magnetospheric emission takes place from the boundary of the extended magnetosphere and not from the surface of the pulsar. Tentatively, such a boundary may lie at the corresponding light cylinders which are expected to be beyond r > 6M or x > 3. Since at x = 3 or r = 6M , it is F 1 = 2.74 and 2F 2 = 2.68, then µ(emission) ∼ µ(distant). Hence, the non-relativistic treatments made by Robertson and Leiter [40,41] remain approximately valid even though the basic situation is an example of extreme general relativity. In other words, the magnetic fields near the spinning down BHMs may very well behave like weakly magnetized NSs.

Conclusion remarks
Starting from Ginzburg in 1964 [7], innumerable authors have suggested that the so-called astrophysical BHs might actually be magnetized BHMs supported by radiation pressure, magnetic field, and rotation too (though the term BHM was not used earlier). In recent times, several other more exotic BHMs too have been introduced from the view point of quantum or semi-classical gravity. The present discussion will be valid for them too in case they would be hypothesized to possess intrinsic dipole magnetic field.
Indeed, there have been direct evidences for presence of unusually high organized strong fields around many astrophysical BHCs. Such evidences have accrued from studies of degrees of linear polarization or rotation of the plane of polarization (Faraday Rotation) of radio emissions from around the BHCs. In particular, now, there are evidences for dynamically important magnetic field near Sgr A * , the galactic BHC [52], as well as at the jet launching site of 76 active galactic nuclei [53]. The evidence about strong organized magnetic field in Sgr A * got consolidated in 2015 from detection of extremely high degrees of linear polarization in 1.3 mm radio waves [54]. In the same year, Faraday rotation (that is the rotation of the plane of polarization of the emission in the presence of an external magnetic field) revealed presence of unusually strong magnetic field at the jet base of a distant AGN, PKS 1830−211 [55]. Also, one can way back to 2003, when polarimetric observations revealed a B ∼ 10 8 G at the inner accretion disk of the the prototype BHC Cyg X-1 [56]. Such observations are much easier to understand if the pertinent compact objects are magnetized BHMs rather than true BHs having no magnetic fields of their own.
Furthermore, in view of the claim of the presence of gravitational wave echoes in the LIGO signals, the question of differentiating a true BH with a BHM becomes very pertinent. One tool to distinguish a true accreting astrophysical BH from an ultra-magnetized BHM could be through study of the magnetic field structure around the relevant compact object. For a true BH, one may expect the frozen in plasma magnetic field to fall off as B ∼ r −1 . On the other hand, for a magnetized BHM, while far away from the surface B ∼ r −3 , in the immediate vicinity, the field pattern is dramatically asymmertic and complex: the radial field B r ∼ 3 µ r 3 z s , and the polar field B θ ∼ 12 µ r 3 ln z s . In fact, radial field pattern apart, any inference about the dramatic asymmetry of the equator field B e and polar field B p components may suggest existence of magnetized BHMs or "magnetoids" conceived by Ginzburg [13] or giant pulsars conceived by Morrison [9] or MECOs or any other magnetized BHMs.