# A Gravitational Wave Background from Primordial Black Hole Lattices in Matter Dominated Era

## TL;DR

This paper investigates gravitational wave production from primordial black hole lattices during matter domination using numerical simulations and analytical estimates, highlighting the role of black hole fraction in their evolution.

## Contribution

It introduces a detailed simulation approach to study primordial black hole lattices and their gravitational wave emissions during matter-dominated era.

## Key findings

- Black hole fraction significantly influences PBHL evolution
- Primordial black holes move at relativistic speeds during expansion
- Gravitational wave emission is confirmed through simulations and analysis

## Abstract

We use the wide-used \textsf{Einstein Toolkit} to solve the Einstein constraints and then simulate the expansion of primordial black hole lattices (PBHLs) with different value of $f_{\mathrm{PBH}}$ and $m_{\mathrm{PBH}}$. We find that $f_{\mathrm{PBH}}$ plays an important role during the evolution of PBHLs. Since the motion of primordial black holes (PBHs) caused by the expansion of PBHLs occurs at speeds close to that of light, we expect the emission of gravitational waves (GWs) during the expansion of PBHLs. We use both analytical estimates and numerical simulations to cross check the production of GWs in expanding PBHLs.