Magnetic fields are ubiquitous in the universe – observed on scales ranging from stellar, through galactic and beyond – and are key to the physics of dramatic astrophysical objects such as pulsars and active galactic nuclei. Meanwhile, the origin of large-scale magnetic fields is still a topic of great debate in the cosmological literature.
Our recent CQG article presents a new family of exact solutions to the Einstein-Maxwell equations for cosmological magnetic fields. These solutions are both inhomogeneous and anisotropic, with the magnetic field having nontrivial dependence on both time and cylindrical radius. While research on astrophysical magnetic fields often employs numerical methods to deal with intrinsically complicated settings, exact solutions in idealized conditions can serve as important guides.
Our starting point is the static, cylindrically symmetric spacetime known as Melvin’s magnetic universe, which has wide-ranging applications in the literature. For example, the horizon of a Kerr black hole in a Melvin background expels magnetic flux as the limit of maximal rotation is approached. More exotically, the quantum decay rate of a magnetic field due to black hole pair production is given by the Euclidean action of the Melvinized C-metric. In higher dimensions, `fluxbrane’ generalizations of the Melvin spacetime are of great interest in the context of string theory.
In cosmology, a Melvin magnetic field interacts with the expansion of the universe. In our solutions the expansion is driven by a time dependent scalar field – a perfect fluid with w=1 equation of state. We also allow for a dilaton coupling between the scalar and electromagnetic field, as one finds in e.g. Kaluza-Klein compactifications or string theory.
The resulting dynamics depends on whether the dilaton coupling exceeds a certain critical value. For small coupling, we find that the magnetic field becomes increasingly concentrated near the symmetry axis as the universe expands, with an inward flux of stress-energy. For large coupling, on the other hand, the magnetic field disperses. An electric field circulating around the symmetry axis also reverses direction at critical coupling.
There are many interesting directions for follow-ups to this work. Two goals would be finding cosmological Melvin spacetimes for all values of the equation of state parameter, and learning how to magnetize cosmological black hole solutions.
The plot shows the magnetic flux enclosed by circles of increasing radius around the symmetry axis at a number of time steps.
As the universe expands, with increasing time, the flux becomes more concentrated near the symmetry axis, approaching its asymptotic value at smaller radii.”
About the authors
David Kastor and Jennie Traschen are faculty members at the Amherst Center for Fundamental Interactions, Physics Department, University of Massachusetts
Read the full article: Class. Quantum Grav. 31 075023
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