Schwarzschild scalar wigs: spectral analysis and late time behavior

Using the Green’s function representation technique, the late time behavior of localized scalar field distributions on Schwarzschild spacetimes is studied. Assuming arbitrary initial data we perform a spectral analysis, computing the amplitude of each excited quasi-bound mode without the necessity of performing dynamical evolutions. The resulting superposition of modes is compared with a traditional numerical evolution with excellent agreement; therefore, we have an efficient way to determine final black hole wigs. The astrophysical relevance of the quasi-bound modes is discussed in the context of scalar field dark matter models and the axiverse.