# Singular Vertices in the Strong Coupling Phase of Four--Dimensional Simplicial Gravity

## TL;DR

This paper investigates four-dimensional simplicial gravity, focusing on singular vertices in the strong coupling phase, and explores phase transition behavior and topology changes through numerical simulations.

## Contribution

It introduces the analysis of singular vertices in 4D simplicial gravity and links their disappearance to a phase transition, also examining topology changes from sphere to torus.

## Key findings

- Singular vertices are prominent in the strong coupling phase.
- The phase transition correlates with the disappearance of singular vertices.
- Topology change from sphere to torus is studied.

## Abstract

We study four--dimensional simplicial gravity through numerical simulation with special attention to the existence of singular vertices, in the strong coupling phase, that are shared by abnormally large numbers of four--simplices. The second order phase transition from the strong coupling phase into the weak coupling phase could be understood as the disappearance of the singular vertices. We also change the topology of the universe from the sphere to the torus.