Scalar field confinement as a model for accreting systems

We investigate the possibility to localize scalar field configurations as a model for black hole accretion. We analyze and resolve difficulties encountered when localizing scalar fields in General Relativity. We illustrate this ability with a simple spherically symmetric model which can be used to study features of accreting shells around a black hole. This is accomplished by prescribing a scalar field with a coordinate dependent potential. Numerical solutions to the Einstein-Klein-Gordon equations are shown, where a scalar filed is indeed confined within a region surrounding a black hole. The resulting spacetime can be described in terms of simple harmonic time dependence.