Accretion of multipolar massive complex scalar field packets by a Schwarzschild black hole

Abstract

We study the finite-time accretion of complex massive scalar wave packets by a Schwarzschild black hole in the test-field regime, with parameters motivated by ultralight fuzzy dark matter around supermassive black holes. Our goal is to determine how the scalar content of a localized configuration is redistributed after interacting with the black hole, and which spectral and multipolar components are more efficiently absorbed. We decompose the Klein--Gordon field into independent multipolar sectors and evolve nearly monochromatic Gaussian packets mode by mode, reducing the problem to a set of 1+1 dimensional evolutions. Accretion is quantified with the flux of the conserved Noether current through the horizon surface, providing a direct measure of the scalar charge absorbed by the black hole. For a carrier radial wavenumber $k_0$ and multipole index $\ell$, we construct accretion-efficiency maps in the $(k_0,\ell)$ plane that contain the fraction of accreted modal charge. These maps exhibit a transition between inefficient, partial, and efficient accretion regimes, which we relate to the structure of an effective potential. We show that the process is controlled by the ratio between the Schwarzschild radius $R_s$ and the reduced Compton wavelength $\lambdabar_C$. For $R_s \lesssim \lambdabar_C$, the transition is broad and dominated by the angular momentum barrier, while for $R_s > \lambdabar_C$ it sharpens across a narrower range of $k_0$ and a partial-accretion floor emerges at low $k_0$. These results provide a time-domain, Noether-charge-based classification of black hole accretion for massive scalar wave packets.