Scalar Tsunamis from Black Hole Formation

Stars and other macroscopic objects may be surrounded by potentially large field configurations of very light scalars coupled to ordinary matter. If the star ends in a black hole, e.g. via a supernova or a neutron star merger, the source vanishes, and the field is released. In this paper, we improve on previous estimates for the field configurations arriving at large distances by including the effects of general relativity and an improved modelling of the initial field configurations. The total amount of energy released is typically of the same order of magnitude as suggested by simple flat space estimates. The spectrum receives noticeable corrections.

💡 Research Summary

The paper investigates the phenomenon that occurs when a massive astrophysical object—such as a star undergoing a supernova or a binary neutron‑star merger—collapses into a black hole (BH). If the object is surrounded by a large configuration of an ultra‑light scalar field that is sourced by its ordinary matter, the disappearance of the source at BH formation releases the stored field energy in the form of a propagating “scalar tsunami”. The authors improve upon earlier flat‑space estimates by explicitly evolving the scalar field in the curved spacetime of a static Schwarzschild black hole and by considering a richer set of initial field configurations.

Model and Initial Conditions
The scalar is taken to be a real, essentially massless field ϕ with a tiny mass mϕ≲10⁻²⁵ eV, so that dispersion over astrophysical distances is negligible. The field is minimally coupled to gravity, and any self‑interactions or couplings to matter are encoded solely in the initial conditions. Four static profiles are studied: (i) a Yukawa‑like 1/r profile, (ii) a homogeneous charged sphere, (iii) a compact (R−r)³ distribution, and (iv) a thin spherical shell. Two dynamical variants are also introduced: an “ingoing‑only” wave obtained by imposing ψ̇=ψ′ on the static profile, and a contracting charged sphere with a prescribed collapse velocity v. These configurations aim to capture possible pre‑collapse field structures that could arise from Yukawa couplings, screening mechanisms, or simple collapse dynamics.

Black‑Hole Background and Evolution Equation
The background metric is Schwarzschild: ds² = f(r)dt² – f(r)⁻¹dr² – r²dΩ² with f(r)=1−rH/r, where rH=2GM is the horizon radius. For a spherically symmetric field the Klein‑Gordon equation reduces to
  ¨ϕ – f(r) r⁻² ∂r