Magnetic brane solutions in Gauss–Bonnet–Maxwell massive gravity

Magnetic branes of Gauss–Bonnet–Maxwell theory in the context of massive gravity is studied in detail. Exact solutions are obtained and their interesting geometrical properties are investigated. It is argued that although these horizonless solutions are free of curvature singularity, they enjoy a cone-like geometry with a conic singularity. In order to investigate the effects of various parameters on the geometry of conic singularity, its corresponding deficit angle is studied. It will be shown that despite the effects of Gauss–Bonnet gravity on the solutions, deficit angle is free of Gauss–Bonnet parameter. On the other hand, the effects of massive gravity, cosmological constant and electrical charge on the deficit angle will be explored. Also, a brief discussion related to possible geometrical phase transition of these topological objects is given.