Magnetic Fields in an Expanding Universe

Abstract

We find a solution to $4D$ Einstein-Maxwell theory coupled to a massless dilaton field describing a Melvin magnetic field in an expanding universe with 'stiff matter' equation of state parameter $w=+1$. As the universe expands, magnetic flux becomes more concentrated around the symmetry axis for dilaton coupling $a<1/\sqrt{3}$ and more dispersed for $a>1/\sqrt{3}$. An electric field circulates around the symmetry axis in the direction determined by Lenz's law. For $a=0$ the magnetic flux through a disk of fixed comoving radius is proportional to the proper area of the disk. This result disagrees with the usual expectation based on a test magnetic field that this flux should be constant, and we show why this difference arises. We also find a Melvin solution in an accelerating universe with $w=-7/9$ for a dilaton field with a certain exponential potential. Our main tools are simple manipulations in $5D$ Kaluza-Klein theory and related solution generating techniques. We also discuss a number of directions for possible extensions of this work.

17 pages, 2 figures; v2 - references added

References in corpus (5)

• Charging axisymmetric space-times with cosmological constant
• Thermodynamics of Magnetised Kerr-Newman Black Holes
• Dynamics of intersecting brane systems -- Classification and their applications --
• Embedding hairy black holes in a magnetic universe
• Ergoregions in Magnetised Black Hole Spacetimes

Cited by in corpus (7)

• Dirac equation and the Melvin Metric
• Generation of large-scale magnetic fields, non-Gaussianity, and primordial gravitational waves in inflationary cosmology
• Melvin Magnetic Fluxtube/Cosmology Correspondence
• Uniqueness of dilaton Melvin-Schwarzschild solution
• Uniqueness of dark matter magnetized static black hole spacetime
• Time-Dependent Warping and Non-Singular Bouncing Cosmologies
• Magnetized dynamical black holes