Dynamical Formation of Scalarized Black Holes and Neutron Stars through Stellar Core Collapse

In a certain class of scalar-Gauss-Bonnet gravity, the black holes and the neutron stars can undergo spontaneous scalarization—a strong gravity phase transition triggered by a tachyonic instability due to the nonminimal coupling between the scalar field and the spacetime curvature. Studies of this phenomenon have, so far, been restricted mainly to the study of the tachyonic instability and stationary scalarized black holes and neutron stars. To date, no realistic physical mechanism for the formation of isolated scalarized black holes and neutron stars has been proposed. We study, for the first time, the spherically symmetric fully nonlinear stellar core collapse to a black hole and a neutron star in scalar-Gauss-Bonnet theories allowing for a spontaneous scalarization. We show that the core collapse can produce scalarized black holes and scalarized neutron stars starting with a nonscalarized progenitor star. The possible paths to reach the end (non)scalarized state are quite rich leading to interesting possibilities for observational manifestations.

Figure 1

Possible outcomes of stellar core collapse in SGB gravity.

Figure 2

Central densities (top panel) and central values of redshift (bottom panel) of supernova progenitors $z12$ (blue line) and $z40$ (yellow line) [36] as functions of time in GR. The formation of a black hole is numerically defined to form as central redshift $e^{\mathrm{\Phi }}<0.01$.

Figure 3

(scenario “$\epsilon =-1$: CC-$\phi \mathrm{NS}$”) Temporal snapshots of scalar field $\phi$ and fluid velocity $v$ as functions of the distance from the core $r=0$ for the $z12$ progenitor are plotted in the upper panel. In the lower panel, the evolution of the central value of the scalar field ${\phi }_c$ and the scalar charge $r\phi$ taken at a very large distance, 50 000 km, are displayed. Markers in the bottom panels indicate the time of snapshots having the same colors in the corresponding upper panels. We have taken $\epsilon =-1$, $\lambda =80$, and $\beta =7000$.

Figure 4

(scenario $\epsilon =1$: CC-NS-$\phi \mathrm{BH}$) Temporal snapshots of scalar field $\phi$ as a function of the distance from the core $r=0$ is plotted for the $z40$ progenitor in the upper panel. In the lower group of panels, central value of scalar field ${\phi }_c$ and the scalar charge $r\phi$ are displayed as functions of time. The notations are the same as in Fig. 3. We have taken $\epsilon =1$, $\lambda =30$, $\beta =20000$.

Figure 5

(scenario $\epsilon =-1$: CC-$\phi \mathrm{NS}$-BH) The same as Fig. 4 but for $\epsilon =-1$, $\lambda =40$, $\beta =25000$. Scalarization of protoneutron star reveals (light red and yellow curves in the upper panel); nonetheless, once the black hole is formed, the scalar field condensates into the event horizon. Descalarization is apparent as shown by the disappearance of the scalar charge after a period of scalarized protoneutron star stage (blue line in the bottom panel).

Figure 6

The scalar radiation emitted during core collapse for the cases presented in Figs. 3, 4, and 5. $E_s(t)$ is practically independent of $r$ for large distances, and in the figure, it is extracted at the same point as the scalar charge, i.e., at 50 000 km. The insets represent a magnification around the most interesting regions for each case.