Focus: Magnetic Fields Smooth Space

Phys. Rev. Focus 7, 27
Magnetic field lines do not like to bend, so when the space around them becomes warped by large masses, the fields fight back.

Magnetic field lines do not like to bend. When you try to press two magnets together the wrong way, you feel this tendency directly–the field lines resist being squashed to the sides. This magnetic “tension” may have surprising effects when space itself warps, according to a paper in the 11 June PRL. The author finds that when spacetime bends in response to matter, the magnetic field lines push back and try to flatten spacetime. This “magnetocurvature” effect would be strongest when spacetime is most strongly curved–near neutron stars and black holes, and in the very early Universe. Magnetocurvature effects might be measurable in gravitational radiation reaching Earth; they also seem to exclude some theories of the Universe’s earliest moments.

We expect magnetic fields near large objects coursing with electric currents, like the Sun, but astronomers have also indirectly observed fields far from stars and galaxies. “We see magnetic fields everywhere,” says Christos Tsagas of Portsmouth University in the UK. “We don’t know how these fields were created,” he adds, but since they’re so common, many cosmologists believe they’ve been around since shortly after the big bang. When the Universe was less than a million years old, the fields may have been 1000 times larger than those in our Galaxy today.

To find out how magnetic fields might affect the evolution of the early Universe, Tsagas put magnetic fields into the standard equations for general relativity. Because of the simplicity and symmetry of the early Universe at the largest scales, he was able to use the “full” theory of relativity, without approximations. Tsagas found that the magnetic tension in bent magnetic field lines tends to flatten the surrounding space. Researchers often assume that the fields were too weak to have much effect, but Tsagas’s results suggest that whenever the curvature of space is large, even a small field can have an effect.

According to inflation theories, the Universe experienced an incredibly rapid growth spurt in the first $10-30$ seconds. Tsagas’s paper suggests that the magnetic fields could prevent this expansion in some models of inflation, so those models may fail when magnetic fields are accounted for.

If magnetic fields tend to flatten space, they might reduce the amplitude of gravitational radiation, which is an undulation in spacetime. That effect might be seen in future gravitational wave observatories, though it is probably too small to be picked up with the first generation of detection technology. The work also suggests that theoretical models of neutron stars and other compact objects may need to include magnetocurvature, since they often involve both large magnetic fields and heavily curved spacetime.

Pedro Ferreira of the University of Oxford is impressed that Tsagas came up with such a seemingly straightforward consequence of general relativity. “I was surprised that no one had done it [earlier],” he says. Thanks to Tsagas’s results, “we understand something fundamental a bit better.”

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