While most of the astronomers believe that the astrophysical BH candidates (BHCs) found in innumerable X-ray binaries and Active Galactic Nuclei (AGN) are true mathematical BHs possessing event horizons (EHs) 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 black hole mimickers (BHMs), which are almost as compact as BHs (R ≈ Rs = 2M) but non-singular and without exact EHs. The radius of a BHM may be expressed as:
R = (1 + ϵ) 2M; ϵ <<1 …. (1)
whereas, for an exact BH, one has ϵ = 0 and R = 2M. Here R and R_s represent the (areal) radius of the compact object and the Schwarzschild radius respectively (units with G = c = 1). Technically, one basic difference between a true BH and a BHM can be expressed through the concept of gravitational redshift around the compact objects:
and on the surface of the compact object:
For a BHM, one finds
Z_s = ϵ^(–1/2) – 1 ≈ ϵ^(–1/2) …. (4) (note: ‘_’ is base)
For a mathematical true BH, one must have z_s = ∞ while for a BHM, though z_s is finite, it can be arbitrarily high: 1 << z_s < ∞.
It is important here to take note of a crucial aspect which is common to both a true BH and its mimicker. Both of them reside within another mathematical surface known as the photon sphere, see Figure 1, that is situated at Rp = 3M, and zs = zp = √3 − 1 ≈ 0.732.
In contrast, for a typical NS, one has z_s ∼ 0.15, and as if the surface gravity of the photon sphere is 5 times stronger than that of a neutron star (NS) . The surface gravity of the photon sphere is already so strong that, on the photon sphere, photons can move in unstable closed circular orbits. In contrast, the circular orbits of finite rest mass particles around a BH or a BHM end at R = 3, R_s = 6M, and this defines the Innermost Stable Circular Orbit (ISCO). Within the ISCO for a non-magnetic BH or BHM, material particles tend to accrete in radial directions and in near free fall.
“It is interesting to note that, not only a true BH (R = 2M) or an ideal BHM (R ≈ 2M), but any compact object whose radius is R ≤ 3M would generate a shadow of the same size. Thus, the so-called image of the supposed BHC must be due to emission from the surrounding plasma beyond the photon sphere/photon ring.”Wrote authors of the study
Within the photon sphere, not only material particles, but even photons tend to preferentially move inward, as the angle of the escape cone shrinks rapidly. In order to escape from the interior of the photon sphere, a photon must ejected in a perfectly radially outward direction. And the probability of escape diminishes rapidly as (1 + z)¯2 while z → ∞ as r → 2M. It is for this reason that the photon sphere acts as a “virtual EH” for the BH and its mimicker. Thus, the compact object looks almost “black” to a far away astronomer.
Now, Cuesta and colleagues in their recently published paper, emphasized the fact that it is not possible to detect any EH directly:
“Recently, several ways of verifying the existence of black hole horizons have been proposed. We show here that most of these suggestions are irrelevant to the problem of the horizon, at best they can rule out the presence of conventional baryonic matter in the outer layers of black hole candidates. More generally, we argue that it is fundamentally impossible to detect in electromagnetic radiation direct evidence for the presence of a black hole horizon. This applies also to future observations, which would trace very accurately the details of the spacetime metric of a body suspected of being a black hole. Specific solutions of Einsteins’s equations lack an event horizon, and yet are indistinguishable in their electromagnetic signature from Schwarzschild black holes.”— said Cuesta lead author of the study.
For an idealized Schwarzschild BH or its mimicker, the radius of the shadow is (see Figure 2): Rshadow = 3√ 3M, if R ≤ 3M, or z_s ≥ 0.732.
Since it is the shadow of the photon sphere (z_p ≈ 0.732) that the astronomer can detect, even a fat BHM having a radius just smaller than the photon sphere, say R = 2.99M, will yield an exterior shadow of the same size Rshadow = 3√ 3M. In view of this rather unexpected fact, no telescope can distinguish between: (i) a true BH (R = 2M) or (ii) an ideal BHM (R ≈ 2M), (iii) even a crude fat BHM (R ≤ 3M). The shadow size would be different from these class of objects only when the radius of the compact object would be larger than its photon sphere (R > 3M) and zs < zp ≈ 0.732, for instance, for a NS, one will have
R_shadow = (1 + z_s)R; if R > 3M, or z_s < 0.732
Thus, the shadow/image of a NS having a radius of 10 km and z_s = 0.15 will appear as a circle of radius 11.5 km. In contrast, for a white dwarf having z_s << 1, there will hardly be any enhancement in the size of the shadow/image.
They didn’t stop here, they also carried out detailed study on the radial variation as well as significant angular asymmetry of magnetic field structure near the compact object which they think might differentiate a theoretical black hole from a astrophysical BH mimicker in future observations. They also hypothesized that some BHMs 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. I know some of you are confused and some of you are damn curious to know about that BHM. But, please keep little patience. I want you to understand total concept of this mimicker. So, we have to explore answers of some impossible questions for it.. Lets start with first one.
Can Neutron Star Mimic To Be A Black hole?
Gravitational waves (GWs) generated from the trembling of the new born unsteady photon sphere travel both outward and inward. The outward moving GWs may exhibit as ring down waveform. If the underlying new born compact object would be a true vacuum BH, it would gulp down all inward moving GWs. In such a case, external telescopes would not detect any subsequent GW emission for the given event. But, in that case, the underlying compact object is a EH less BHM. The inward travelling GWs will initially remain trapped between its surface and the photon sphere. However, part of the trapped GWs would diffuse out later following repeated reflections from the physical surface of the BHM. In such a case, there might be subsequent GW echoes. There have been some weak evidences for GW echoes associated with three cases of GW detection: GW150914, GW151226, and LVT151012. In comparison, there has been stronger evidence for GW echoes for the binary neutron star merger event GW170817. Thus, tentative detection of GW late echoes might suggest that the compact objects formed by the coalescence of either so-called BHs or even NS might be BHMs having physical surfaces and not vacuum BHs possessing EHs.
Can Magnetic Fieldless Spinning Black Holes Act As Strongly Magnetized Pulsars?
It is well known that, when any conductor moves in an external magnetic field, it develops an induced electromagnetism. If the conducting sphere itself is magnetized, it can develop an induced electric field even in the absence of any exterior magnetic field. This is the reason that spinning magnetized NSs act as electromagnetic pulsars. The energy radiated by pulsars originate from their immense rotational kinetic energies. By taking this cue, in order to explain the source of energy of ultra-relativistic jets associated with astrophysical BHs, it was assumed that spinning/rotating BHs too may act like spinning NSs or pulsars.
Any Ideas About Magnetized Black Hole Mimickers?
Yeah, there are several ideas about magnetized black hole mimickers. The first was proposed by Hoyle and Fowler in 1963. According to which the centre of the quasars contain Radiation Pressure Supported Supermassive Stars and that the luminosity of the quasars may be ascribed to the huge luminosity of such supermassive stars radiating at their Eddington limit. After 6 years, Goldreich and Julian developed the theory of pulsars as spinning strongly magnetized NSs where the source of energy is the rotational kinetic energy of the NS, and neither any accretion process nor surface luminosity of any star. Then in 1977, Ginzburg and Ozernoi coined a term “Magnetoids” to describe such spinning magnetized supermassive stars, supported by radiation pressure, magnetic field and centrifugal repulsion. Some authors instead chose a term “spinar” to describe such non-singular BH candidates. In 2008, Lipunov and Gorbovskoy defined: “A spinar is a collapsing object with quasi-equilibrium. Its equilibrium is maintained by the balance of centrifugal and gravitational forces and its evolution is determined by its magnetic field.”
However, all such studies are, at the best, sketches and no comprehensive general relativistic study was ever made. In particular, such studies did not address the crucial questions such as: (i) How massive stars or supermassive gas clouds, during their continued gravitational collapse, end up as non-singular compact objects when it is commonly believed that continued gravitational collapse must lead to formation of exact BHs? (ii) What is the source of central energy generation of such massive compact objects? Central nuclear burning or something else? Authors of the current study thinks that the Referees or Editors behind such papers published in prestigious journals did not raise such issues either.
This theoretical vacuum was largely filled in 2000-10, and a much more solid framework was realized for existence of quasi-static ultra-magnetic compact objects, the so-called Magnetospheric Eternally Collapsing Objects (MECOs) (and that’s what the topic of this current study). It turned out that MECOs are essentially extremely general relativistic versions of Radiation Pressure Supported Stars whose concept was originally given by Hoyle and Fowler. 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, once the massive star contracts below its photon sphere which is a quasi-event horizon, the heat and radiation generated by the collapse process get trapped by self-gravity. One notes that, while the photon sphere has z = 0.732, the EH should have z = ∞.
Thus, the journey from the photon sphere upto the supposed EH should be an infinite trek in terms of traversing through strength of gravity. It can be seen that the outward force due to trapped radiation increases much faster, that is ∼ (1 + z_s)², than the relevant Eddington luminosity ∼ (1 + z_s). Consequently, at some appropriately high zs >> 1, there should a quasi-equilibrium upon attainment of Eddington luminosity by the collapsing object.
While the idea of MECO eliminates the formation of exact BHs on the strength of inevitable generation of Eddington limited radiation pressure supported stars, it may be relevant to note that nonlinear electrodynamics too might prevent formation of exact BHs.
Do we have any astrophysical Evidences For MECOs?
There are many actually, you can refer this paper for more details. I am sharing one with you. In 2006, astrophysicists discovered “Fermi bubbles”, that are two colossal elliptical gamma ray emitting blobs extending around 10 kpc above and below the GC. The blobs are filled with very hot magnetized plasma. Even 14 years post their discovery, “the formation mechanism of the bubbles is still elusivis”, though there are several conjectures. Yet, the mirror-like symmetry of the bubbles around the GC suggests that they resulted from some super gigantic explosion at the GC which injected an energy may be as large as 1055¯56 ergs some 5 to 6 Myr ago. It is tempting to assume that it was an explosion of the MECO Sgr A*. Such an historic explosion may not be any Coronal Mass Ejection, but may have been triggered by additional instability generated by the accretion of a massive star or a small star cluster onto the MECO.
Any Direct Evidences For MECOs?
In 2006, Schild, Leiter and Robertson presented evidence that the inner edge of the accretion disk of the quasar QSO 0957+561, appearing as a bright luminous ring, is located at r_i ∼ 35R_s = 70M, when, for an unmagnetized BH, one expects r = 3R_s = 6M. Accordingly, they concluded that QSO 0957+561 contains a MECO in lieu of a BH. They also inferred the existence of “hourglass shaped” outflow of plasma from around the central compact object, and interpreted this outflow to be guided by large scale organized dipole magnetic fields of the MECO.
Later, a similar inner structure was found in another quasar Q2237. Further, studies of 55 more quasars too indicated the presence of inner magnetic field controlled structures, similar to the one found in QSO 0957. Such studies suggest that all quasars might be containing MECOs in lieu of BHs. The detailed physics of emission of X-ray and radio emission from Sag A∗ , the BH candidate at the centre of our galaxy, the Milky Way, may too be well understood in the MECO paradigm. In the current paper, authors have also discussed that there is direct evidence for presence of unexpectedly high large scale partially organized magnetic fields around the compact objects of innumerable AGNs as well as for Sgr A∗ , the supposed supermassive BH in our GC. Further, there is evidence for a superstrong magnetic field at the inner accretion disk of the compact object in Cygnus X-1. In fact, the so- compact object in Cygnus-1 may have a dipole magnetic moment of ∼ 1030 Gcm³ , which led to the idea that it is a MECO rather than a true BH.
How will you distinguish true black holes from MECO’s?
It has been recently suggested that one should use the magnetic field pattern around accreting compact objects to test whether they are true BHs or not. While uncharged BHs possessing EHs do not possess any magnetic field, the plasma accreting onto them can possess magnetic fields and which may vary as ∼ r¯1. In contrast, even uncharged BHMs may possess their 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 magnetic field in the plasma (∼ r¯1) is expected to be much weaker to the intrinsic field of the BHM.
Cuesta and colleagues highlighted the fact that, in the immediate vicinity of the BHM, the field pattern should be much more complex than the one of a NS: B ∼ r¯3. This is because while the radial field is Br ∼ 3 (µ/R³) × z_s, the polar field is Bp ∼ 12 (µ/R³) × 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/Ln z_s. Therefore, even an ultra magnetized BHM may behave as a NS whose magnetic field could be weaker than the same of young NSs by a factor of order 10⁴.
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Reference: 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://link.springer.com/article/10.1007/s10509-020-03913-3 https://doi.org/10.1007/s10509-020-03913-3
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