Why everyday magnetism doesn’t matter gravitationally
In general relativity, the source of spacetime curvature is the stress-energy tensor, and an electromagnetic field contributes to it through its energy density (roughly B²/2μ₀ for a magnetic field). Even a strong lab magnet — a few tesla — has an energy density that’s utterly negligible compared to, say, the rest-mass energy density of the magnet’s own iron core. The curvature it produces is many, many orders of magnitude below anything measurable. Gravity is just an extraordinarily weak force per unit of “ordinary” energy.
Where it stops being negligible
In astrophysical settings the field strengths and energy densities involved make the electromagnetic stress-energy tensor a genuine player in the Einstein field equations rather than a rounding error. A few examples:
- Magnetars: surface fields of 10^10–10^11 tesla. At these strengths, the magnetic energy density becomes comparable to nuclear energy densities, and the field’s contribution to the star’s structure and stress-energy is significant — magnetar equations of state have to include the field’s pressure (anisotropic, since magnetic pressure is different along vs. across field lines).
- Neutron star interiors/magnetospheres: strong internal fields can measurably affect the star’s shape (magnetically induced ellipticity) and are relevant to models of glitches and crust fracturing.
- Charged/magnetized black hole solutions (Kerr-Newman, magnetized Kerr): exact GR solutions exist where the EM field is not a test field but a full source term shaping the metric itself.
- Accretion disks and jets around compact objects: magnetic stresses (via magnetohydrodynamics) drive angular momentum transport and jet launching, and in the innermost regions the field energy density can be a non-trivial fraction of the total stress-energy budget feeding the local curvature.
The general pattern: whenever B²/2μ₀ becomes comparable to matter’s rest-energy density (or to nuclear/radiation energy densities), the EM stress-energy tensor stops being a perturbative afterthought and has to be solved self-consistently with the metric — that’s the threshold “extreme energy density” is really pointing at.
“Sighs” I was just making topic conversations, no declaration came with this.
If I am not welcome to post anything newly discovered “scientifically” just tell me, don’t do it this way. ~QS
My apologies QS, I thought you wanted to talk about time travel…
I do, but I talk about everything?
My interests are pulled in many ways, no one subject hold my attention for too long.
I need multiple outlets to express myself. I am sorry also. Please forgive me.
~QS
Apocalypse, spot on.
(LIQUID), demonstrated an another type of hall effect.
I think the properties of magnets are one of the coolest things, they have pushed us forward in sooo many cool technologies & keep making cutting edge advances in nearly everything!
~QS