Primordial black hole and wormhole formation by domain walls

TL;DR

This paper analyzes PBH and wormhole formation from inflation-nucleated spherical domain walls in a radiation-dominated FRW universe. It combines a detailed numerical GR+scalar-field framework with adaptive mesh refinement to map how wall size controls subcritical and supercritical outcomes, deriving precise initial PBH masses $M_{BHi}(R)$ and tracking subsequent accretion that doubles outer BH masses over time. The results reveal distinct dust vs. radiation behaviors: subcritical accretion is modest in radiation with a scaling factor $F\approx3.8$, while supercritical walls generate a wormhole with two BH horizons, where outer masses can reach roughly $2$–$2.8$ times the inner masses, and an upper bound on initial BH mass tied to the cosmological horizon. These findings shape the PBH mass spectrum and have potential implications for early-universe astrophysics, gravitational waves, and GRB-like fireball phenomena.

Abstract

In theories with a broken discrete symmetry, Hubble sized spherical domain walls may spontaneously nucleate during inflation. These objects are subsequently stretched by the inflationary expansion, resulting in a broad distribution of sizes. The fate of the walls after inflation depends on their radius. Walls smaller than a critical radius fall within the cosmological horizon early on and collapse due to their own tension, forming ordinary black holes. But if a wall is large enough, its repulsive gravitational field becomes dominant much before the wall can fall within the cosmological horizon. In this "supercritical" case, a wormhole throat develops, connecting the ambient exterior FRW universe with an interior baby universe, where the exponential growth of the wall radius takes place. The wormhole pinches off in a time-scale comparable to its light-crossing time, and black holes are formed at its two mouths. As discussed in previous work, the resulting black hole population has a wide distribution of masses and can have significant astrophysical effects. The mechanism of black hole formation has been previously studied for a dust-dominated universe. Here we investigate the case of a radiation-dominated universe, which is more relevant cosmologically, by using numerical simulations in order to find the initial mass of a black hole as a function of the wall size at the end of inflation. For large supercritical domain walls, this mass nearly saturates the upper bound according to which the black hole cannot be larger than the cosmological horizon. We also find that the subsequent accretion of radiation satisfies a scaling relation, resulting in a mass increase by about a factor of 2.

Figures (22)

• Figure 1: Trajectories of five walls in dust background (left panel, with $t_{\sigma}\approx74$) and radiation background (right panel, with $t_{\sigma}\approx30$), with $r_{i}=3,3.5,3.8,3.9,4$ from the bottom up. $R_{wall}=ar$ is the wall's area radius. Solid curves are obtained from Eq. (\ref{['4']}), and dots are from simulations. We can see that Eq. (\ref{['4']}) works very well in the case of dust background even for walls near the critical regime, where they start inflating.
• Figure 2: $M_{BH}$ as a function of time for two subcritical walls in dust background with $r_{i}=5$ and $6$, and $t_{\sigma}\approx300.$ After the black hole is formed, its mass increases and converges to $M_{BHf}\approx(1/2)r_{i}^{3}$.
• Figure 3: Evolution of the radiation energy density distribution in the case of a subcritical wall with $r_{i}=5$ and $t_{\sigma}\approx300$. The left panel shows $\rho(r)$ at time $t=20.5,24.5,28.5,32.5,40.5$ from the top. The wall (which is not shown in the plot) is at the position where $\rho$ has the minimum value. We can see that rarefaction waves (which will be discussed later) are produced and propagate away from the wall. Meanwhile in the exterior region the energy density decreases as in an FRW universe. A "bump" develops outside the wall and will be cut off later because it will be within the black hole apparent horizon. The right panel shows $\rho(r)$ at time $t=40.5,52.5,72.5,112.5$ from the top. The black hole (which is excised for the last three moments in the plot) is not surrounded by an empty layer as it is in a dust universe. We can see that the energy deficit between the apparent horizon and the unperturbed FRW region is smoothed out with time.
• Figure 4: $M_{BH}$ as a function of time for six subcritical walls in the background of radiation with the same surface tension ($t_{\sigma}\approx300$) but different radii. $r_{i}=5,6,7,8,9\ \hbox{and}10$ from the bottom. Blue curves are from simulations, and dashed red curves are from Eq. (\ref{['accretion']}). For $r_{i}=5$, $\frac{M_{BHf}}{M_{BHi}}\approx1.5$; for $r_{i}=6$, $\frac{M_{BHf}}{M_{BHi}}\approx1.6$; for $r_{i}=7,$$\frac{M_{BHf}}{M_{BHi}}\approx1.8$; for $r_{i}=8,$$\frac{M_{BHf}}{M_{BHi}}\approx1.9$; for $r_{i}=9,$$\frac{M_{BHf}}{M_{BHi}}\approx2.0$; for $r_{i}=10,$$\frac{M_{BHf}}{M_{BHi}}\approx2.0$. The ratio increases to $\sim2$ as we approach the critical regime.
• Figure 5: $M_{BH}$ as a function of time for four subcritical walls in the background of radiation with the same $r_{i}(=5)$ but different surface tension. $t_{\sigma}\approx200,100,50\ \hbox{and}25$ from the bottom. Blue curves are from simulations, and dashed red curves are from Eq. (\ref{['accretion']}). For $t_{\sigma}=200$, $\frac{M_{BHf}}{M_{BHi}}\approx1.5$; for $t_{\sigma}=100$, $\frac{M_{BHf}}{M_{BHi}}\approx1.8$; for $t_{\sigma}=50$, $\frac{M_{BHf}}{M_{BHi}}\approx2.0$; for $t_{\sigma}=25$, $\frac{M_{BHf}}{M_{BHi}}\approx2.0$. The ratio increases to $\sim2$ as we approach the critical regime.