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Primordial black hole formation from collapsing domain walls with full general relativity

Naoya Kitajima

TL;DR

This work investigates primordial black hole formation from collapsing isolated closed domain walls in a Z2 scalar-field model using fully nonlinear 3+1 numerical relativity with CCZ4 and moving-puncture gauge. The authors derive and test a Lorentz-contracted modification to the naive Schwarzschild-threshold criterion, finding that a collapse fraction $f \gtrsim 0.8$ yields black holes, with more than 80% of the initial wall energy ending up in the BH. They extend the analysis to ellipsoidal, nonspherical walls (axis ratios up to 1.5) and find BH formation remains possible, albeit with smaller apparent horizons and energy loss likely due to gravitational waves. The results provide a robust GR benchmark for PBH formation from domain walls and highlight how wall tension, size, and geometry govern PBH formation and potential spin, with implications for early-universe PBH abundances.

Abstract

We study the dynamics of isolated closed domain walls with 3+1 numerical relativity. A closed wall shrinks due to its own surface tension, and its surface energy is converted to the kinetic energy, leading to implosion. Then, it can result in the formation of a black hole. First, we focus on spherically symmetric closed domain walls and clarify whether they finally evolve into black holes. Naively, the wall can collapse if its thickness is smaller than the Schwarzschild radius which is determined by the initial surface energy. Our numerical results support this naive criterion for the black hole formation, and indicate that more than 80% of the initial wall energy falls into the black hole. We also investigate the nonspherical collapse by considering the ellipsoidal configurations for the closed domain walls, and it turns out that black holes can be formed even when the ratio of semi-major to semi-minor axes is 1.5.

Primordial black hole formation from collapsing domain walls with full general relativity

TL;DR

This work investigates primordial black hole formation from collapsing isolated closed domain walls in a Z2 scalar-field model using fully nonlinear 3+1 numerical relativity with CCZ4 and moving-puncture gauge. The authors derive and test a Lorentz-contracted modification to the naive Schwarzschild-threshold criterion, finding that a collapse fraction yields black holes, with more than 80% of the initial wall energy ending up in the BH. They extend the analysis to ellipsoidal, nonspherical walls (axis ratios up to 1.5) and find BH formation remains possible, albeit with smaller apparent horizons and energy loss likely due to gravitational waves. The results provide a robust GR benchmark for PBH formation from domain walls and highlight how wall tension, size, and geometry govern PBH formation and potential spin, with implications for early-universe PBH abundances.

Abstract

We study the dynamics of isolated closed domain walls with 3+1 numerical relativity. A closed wall shrinks due to its own surface tension, and its surface energy is converted to the kinetic energy, leading to implosion. Then, it can result in the formation of a black hole. First, we focus on spherically symmetric closed domain walls and clarify whether they finally evolve into black holes. Naively, the wall can collapse if its thickness is smaller than the Schwarzschild radius which is determined by the initial surface energy. Our numerical results support this naive criterion for the black hole formation, and indicate that more than 80% of the initial wall energy falls into the black hole. We also investigate the nonspherical collapse by considering the ellipsoidal configurations for the closed domain walls, and it turns out that black holes can be formed even when the ratio of semi-major to semi-minor axes is 1.5.
Paper Structure (15 sections, 35 equations, 12 figures)

This paper contains 15 sections, 35 equations, 12 figures.

Table of Contents

  1. Introduction
  2. PBH formation from domain walls
  3. Domain wall model
  4. PBH formation criterion
  5. Numerical setup
  6. 3+1 formalism
  7. Initial condition
  8. Numerical implementation
  9. Numerical results
  10. Spherical collapse
  11. Non-spherical collapse
  12. Discussion
  13. CCZ4 formulation
  14. Validity check
  15. Bounce and prolate ellipsoidal collapse

Figures (12)

  • Figure 1: Spatial profiles of the scalar field (red) and the energy density (blue) for the $Z_2$ domain wall. We set $\lambda=1$.
  • Figure 2: The surface of nonspherically closed domain walls in the cases with oblate (left) and prolate (right) ellipsoids. In this figure, the ratio of the semi-major axis (along $x$-axis) to the semi-minor axis (along $z$-axis) is 1.5.
  • Figure 3: Time evolution of the 2-dimensional profile of the scalar field energy density. Time evolves from upper left to upper right and then from lower left to lower right, corresponding to the coordinate time $vt = (0,10,15,20,25,30)$. Each axis and the color bar are respectively normalized by $v^{-1}$ and $v^{-4}$. Note that the scales of the axes and the color bar are different in each panel. We set $R_0 = 14v^{-1}$ and $v = 0.11M_{\rm pl}$.
  • Figure 4: The profile of the conformal factor $\chi$ (red filled circle) and the lapse $\alpha$ (blue open circle) at the final time of the simulation $t=30v^{-1}$. We set $R_0=14v^{-1}$ and $v=0.11M_{\rm pl}$ ($0.079M_{\rm pl}$) the left (right) panel.
  • Figure 5: The time evolution of the conformal factor $\chi$ (solid) and the lapse $\alpha$ (dashed) evaluated at the center of the simulation box. The initial shell radius is $R_0 = 10v^{-1}$ ($14v^{-1}$) in the left (right) panel.
  • ...and 7 more figures