Assume there is a neutron star with a magnetic field and no net electrical charge. What happens to the magnetic field if it gains some mass and collapses into a black hole?
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2 Answers
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This paper by Lyutikov and McKinney describes this precise scenario. I'll provide a brief summary of their results here.
One of the crucial underlying assumptions made when deriving the no-hair theorem is that the region outside the event horizon is a vacuum. However, a rapidly spinning, magnetized neutron star can induce vacuum breakdown, leading to the existence of self-generated currents in the magnetosphere. That is, an initial spinning dipole field with no external currents evolves into a magnetized black hole supported by currents outside the event horizon. In particular, rotation-induced poloidal currents cause magnetic field lines which originate near the poles of magnetar to "open up" to infinity.
The presence of a conductive plasma in the magnetosphere freezes magnetic field lines into the surface. As the magnetar collapses, the closed field lines are absorbed into the event horizon. However, the open lines, which connect the magnetar surface to infinity, persist and end up connecting the event horizon to infinity. The resulting field relaxes to a split monopole configuration which looks something like this:
Over time, the equatorial current sheet dissipates and the field lines which are anchored to the event horizon are able to "slide off" and the magnetic field decays. However, this process relies on the finite resistivity of the plasma in the magnetosphere, and is slow when compared to the timescale one would naively expect from the no-hair theorem. As a result, magnetized black holes can persist for quite a while even in the absence of externally supplied accretion material.
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3$\begingroup$ This is a truly fascinating story +1! Would it be correct to say that it is a pure speculation with no experimental evidence whatsoever? It all seems to stem from the assumption that "a rapidly spinning, magnetized neutron star can induce vacuum breakdown". Can it really? Has a vacuum breakdown by anything spinning been ever observed? Or can it rather be taking a mathematical model of reality beyond its limits of applicability? $\endgroup$ Sep 6, 2020 at 4:03
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1$\begingroup$ @safesphere The instability of the vacuum outside a rapidly spinning black hole in the presence of a strong magnetic field was explored in a 1977 paper by Blandford and Znejek, and appears to be on fairly firm theoretical footing. My guess is that there is no conclusive observational evidence of this effect yet, but I cannot speak to that with any degree of confidence. $\endgroup$ Sep 6, 2020 at 5:40
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$\begingroup$ so I think I heard you say that the elusive monopole can be formed by the collapse of a magnetar into a black hole... $\endgroup$– MichaelSep 6, 2020 at 19:52
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$\begingroup$ @Michael Not a monopole - a split monopole. Note the directions of the field lines attached to the north hemisphere vs. the south hemisphere. $\endgroup$ Sep 6, 2020 at 19:54
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1$\begingroup$ @Andrew An outside observer would quickly see an apparent horizon, to which the magnetic field lines would be attached. From there, the dissipation would proceed in finite time. $\endgroup$ Sep 7, 2020 at 22:38
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Magnetars are neutron stars where the extremely strong magnetic field originates from something called the magnetohydrodynamic process in the turbulent extremely dense superconducting fluid, that persist even after the neutron star settles into equilibrium.
These fields then persist due to persistent currents in a proton-superconductor phase of matter that exists at an intermediate depth within the neutron star (where neutrons predominate by mass).
https://en.wikipedia.org/wiki/Magnetar
You are asking what would happen after the magnetar would collapse into a Black Hole (actually it needs to gain stress-energy, not mass). I will assume you are asking about a Kerr Black Hole, that is, one that has no magnetic field officially.
Now after the collapse, the new Black Hole would have no magnetic field, that is, outside the Event Horizon, we could not observe any magnetic field. The characteristics of the Black Hole would still be describable by the Kerr metric.
It is very important that the answer to this question depends upon the source of the magnetar's magnetic field. Since that is based on the structure (and internal magnetohydrodynamic processes) of the magnetar, that would be destroyed as the extreme levels of gravity would win over the magnetar's internal structure to the lowest level, the magnetar's inside magnetohydrodynamic structure would eventually be torn into its elementary constituents.
So the answer to your question is that after the collapse, there would be no magnetic field observable outside the Event Horizon.
Just a note, officially, we do not have a clear declaration as of today whether Black Holes themselves could have magnetic fields, though, we have detected magnetic fields around Sagittarius A, near the event horizon, the source of these might just be the accretion disk and not the Black Hole itself.
https://en.wikipedia.org/wiki/Black_hole#cite_note-152
So officially, Kerr type Black Holes do not have a magnetic field, and the fact that the original (before the collapse) astrophysical object is a magnetar does not change this.
answered Sep 5, 2020 at 22:00
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1$\begingroup$ Although this is a similar question, I'm not asking what would happen if a magnetar and a black hole merge. I'm asking what would happen to a magnetar if it simply gained some mass (i.e. meteorite impact) and it's gravitational force became large enough for it to collapse into a black hole. $\endgroup$– AndrewSep 5, 2020 at 22:13
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1$\begingroup$ Suggestion: Clarify that BH means black hole and EH means event horizon. These are not standard acronyms. $\endgroup$– G. SmithSep 5, 2020 at 23:12
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1$\begingroup$ @G.Smith, please help me understand- is the reason that a black hole which formed from a magnetized object has no magnetic field because in the process of collapsing, the field-generating mechanism of the object is destroyed? And should I post this as a question myself? I'm very confused here! $\endgroup$ Sep 6, 2020 at 1:27
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2$\begingroup$ @nielsnielsen "is the reason that a black hole which formed from a magnetized object has no magnetic field because in the process of collapsing, the field-generating mechanism of the object is destroyed?" - Yes, exactly, squashed by gravity. The magnetic field is generated by different charges moving differently, much like the field of an electromagnet, which itself is electrically neutral. Now, put the electromagnet under a powerful hydraulic press… $\endgroup$ Sep 6, 2020 at 3:49
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1$\begingroup$ @Michael The reason is the no-hair theorem. In the absence of external matter, the only parameters which characterize a black hole are its mass, angular momentum, and charge. In the absence of net charge, the black hole is of Kerr type, which does not support a magnetic field. You need external matter for that. $\endgroup$ Sep 6, 2020 at 22:15