Primordial black hole formation from a nonspherical density profile with a misaligned deformation tensor

Understand

We perform the numerical simulation of primordial black hole formation from a nonspherical profile of the initial curvature perturbation $\zeta$.

• We consider the background expanding universe filled with the perfect fluid with the linear equation of state $p=w\rho$ ($w=1/3$ or $1/5$), where $p$ and $\rho$ are the pressure and the energy density, respectively.
• The initial condition is set in a way such that the principal directions of the second derivatives of $\zeta$ and $\triangle \zeta$ at the central peak are misaligned, where $\triangle$ is the Laplacian.
• In this setting, since the linearized density is proportional to $\triangle \zeta$, the inertia tensor and deformation tensor $\partial_i\partial_j \zeta$ are misaligned.