system
Given the following post, respond as if you're commenting on Reddit:
human
Does the magnetic field energy around a magnetar type neutron star have mass?

From wikipedia: A magnetar's 1010 tesla field, by contrast, has an energy density of 4.0×1025 J/m3, with an E/c2 mass density more than 10,000 times that of lead.

If I'm understanding this, it's saying that the energy stored in any given cubic meter of magentic field around a magnetar is 10,000 times the energy of 1 cubic meter of lead converted to energy in accordance with E =mc^2

First off, this completely blows my mind. I didnt realise *anything* could store energy at a higher density than matter besides maybe a black hole.

Second, does this magnetic field energy have mass? Does this mass make the neutron star more massive? Like, from outside the strong field, looking in, is the total mass in a sphere around the neutron star and its magnetic field higher than the mass inside a sphere around only the actual neutron star? 

Could this energy be released quickly?
gpt
**Short answer:** The magnetic field doesn't have mass; it is a massless field. However, the energy stored in the field is very real and can contribute to the overall effective mass of the star. 

**Long answer:** Recalling general relativity, mass *and energy* both curve spacetime, meaning that they contribute to the strength of gravitational fields. For example, a charged battery would register as ever so slightly heavier on a scale than an uncharged battery. This doesn't mean the battery is more massive or that there are more particles of matter present, it means something very different. It means the energy stored in it and that energy is gravitating too. This has funny consequences, like a kugelblitz- since light has energy it will curve spacetime, so it would be possible to create a black hole without any matter by just shining enough light in one spot. 

A strong magnetic field is a bit like this battery too. So, as you say, the very very strong magnetic field of a neutron star results in an energy density higher than the energy density of matter on earth. That's pretty wild. 

For comparison though, a neutron star is about one hundred trillion times the mass density of lead, so even though this magnetic field has an enormous energy density by earth standards (and by objective standards, these are the strongest magnetic fields in the universe), their energy density still pale in comparison to the energy density of neutron star matter. 

As for your last question, the magnetic field energy of neutron stars can be released, and such things have been observed. A handful of phenomena have been linked to rapid releases of magnetic energy from neutron stars, such as soft gamma repeaters. Hypothetical events include neutron star merger crust shattering flare, and explanations for fast radio bursts. All these phenomena use the reservoir of energy in the magnetic field to create high energy astrophysical phenomena, like snapping giant magnetic rubberbands.