Geometry of AdS-Melvin Spacetimes

Abstract

We study asymptotically AdS generalizations of Melvin spacetimes, describing gravitationally bound tubes of magnetic flux. We find that narrow fluxtubes, carrying strong magnetic fields but little total flux, are approximately unchanged from the $\Lambda =0$ case at scales smaller than the AdS scale. However, fluxtubes with weak fields, which for $\Lambda =0$ can grow arbitrarily large in radius and carry unbounded magnetic flux, are limited in radius by the AdS scale and like the narrow fluxtubes carry only small total flux. As a consequence, there is a maximum magnetic flux ${\Phi }_{max}=2\pi /\sqrt{-\Lambda }$ that can be carried by static fluxtubes in AdS. For flux ${\Phi }_{tot}<{\Phi }_{max}$ there are two branches of solutions, with one branch always narrower in radius than the other. We compute the ADM mass and tensions for AdS-Melvin fluxtube, finding that the wider radius branch of solutions always has lower mass. In the limit of vanishing flux, this branch reduces to the AdS soliton.

15 pages

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• Solenoid configurations and gravitational free energy of the AdS--Melvin spacetime
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• Properties of the magnetic universe with positive cosmological constant
• A Minkowski-type inequality in the AdS-Melvin space