The paper works out the geometry, flux, and geodesics of the Melvin magnetic universe with a positive cosmological constant, showing its two-sphere section is compact and carries a conical singularity, with a Freund-Rubin flux compactification as a critical limit.
Solenoid configurations and gravitational free energy of the AdS--Melvin spacetime
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abstract
In this paper we explore a solenoid configuration involving a magnetic universe solution embedded in an empty Anti-de Sitter (AdS) spacetime. This requires a non-trivial surface current at the interface between the two spacetimes which can be provided by a charged scalar field. When the interface is taken to the AdS boundary, we recover the full AdS--Melvin spacetime. The stability of the AdS--Melvin solution is also studied by computing the gravitational free energy from the Euclidean action.
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Properties of the magnetic universe with positive cosmological constant
The paper works out the geometry, flux, and geodesics of the Melvin magnetic universe with a positive cosmological constant, showing its two-sphere section is compact and carries a conical singularity, with a Freund-Rubin flux compactification as a critical limit.