Radially Symmetric Scalar Solitons

A class of noncanonical effective potentials is introduced allowing stable, radially symmetric, solutions to first order Bogomol'nyi equations for a real scalar field in a fixed spacetime background. This class of effective potentials generalizes those found previously by Bazeia, Menezes, and Menezes [Phys.Rev.Lett. 91 (2003) 241601] for radially symmetric defects in a flat spacetime. Use is made of the "on-shell method" introduced by Atmaja and Ramadhan [Phys.Rev.D 90 (2014) 10, 105009] of reducing the second order equation of motion to a first order one, along with a constraint equation. This method and class of potentials admits radially symmetric, stable solutions for four dimensional static, radially symmetric spacetimes. Stability against radial fluctuations is established with a modified version of Derrick's theorem, along with demonstrating that the radial stress vanishes. Several examples of scalar field configurations are given.