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.
Highlights
If a Schwarzschild black hole is taken as the seed, the result of the Harrison transform is a black hole immersed in the Melvin universe [5]
Havrdová and Krtouš have derived the solution by taking the charged C-metric and pushing the black hole far away while keeping the electromagnetic fields finite at the neighbourhood of the acceleration horizon [11]
To reiterate in the closing of this section, a surface complex scalar field of charge e and magnitude η is able to source the Anti-de Sitter (AdS) solenoid of parameters ( B, r0 ) and radius R through
Summary
If a Schwarzschild black hole is taken as the seed, the result of the Harrison transform is a black hole immersed in the Melvin universe [5] This procedure has been generalised to higher dimensions by Ortaggio [6], and extended to include dilaton-type scalar fields by [7,8,9,10]. Havrdová and Krtouš have derived the solution by taking the charged C-metric (which describes a pair of charged accelerating black holes) and pushing the black hole far away while keeping the electromagnetic fields finite at the neighbourhood of the acceleration horizon [11]. In Reference [15], the authors considered a Λ = 0 Melvin universe of finite radius is embedded in flat spacetime.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
