Scalar Tsunamis from Black Hole Formation

TL;DR

The paper addresses whether a large, nearly massless scalar field surrounding a star can be released as a Tsunami when the star collapses to a black hole, and how general relativity alters the signal. It evolves various initial field configurations in a Schwarzschild background using tortoise coordinates and quantifies both the total energy escaping and the spectral content, comparing against flat-space estimates. The main findings show that the total energy released remains of the same order as flat-space expectations, but the spectrum is notably redshifted and shaped by the black-hole potential, with low-frequency modes more reflected and high-frequency modes more transmitted. The work highlights the importance of GR in predicting transient signals for terrestrial detectors and informs constraints on ultra-light scalars by connecting initial-field configurations to observable spectra in a strong-gravity setting.

Abstract

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.

Figures (14)

• Figure 1: Example of static (blue) and dynamical (green) initial conditions for the Yukawa-like case in arbitrary units. The left (right) plot shows the field value (time derivative) at $t=0$, when the BH forms. The collapse velocity was taken to be $v=0.4$, while the initial and final radii are taken to be $R_i=5$, $R_f=1$; the collapse then begins at $t_\star=-10$.
• Figure 2: BH potential in Tortoise coordinates for $r_H=1$ in arbitrary units.
• Figure 3: Distribution of the energy as a function of the distance from the horizon in tortoise coordinates for an initial Yukawa and Compact profiles with $g_{Y,C}=1$. All quantities are expressed in units of $r_H$, which was fixed to $r_H=1$ for the plots.
• Figure 4: Spatial distribution of the field at different times for an initial Yukawa-like distribution. The left panel uses tortoise coordinates, whereas the right one uses Schwarzschild coordinates.
• Figure 5: Left: Time evolution of the field at different space points for an initial Yukawa-like distribution. Right: Power spectral density for the Yukawa-like and different homogeneous charged spheres initial configurations. The curved and flat space calculations are shown with solid and dashed lines, respectively.