# Scaling Structures in Four-dimensional Simplicial Gravity

## TL;DR

This paper explores the geometric structures of four-dimensional spacetime in simplicial quantum gravity by analyzing boundary volume distributions across different coupling phases, revealing distinct scaling behaviors.

## Contribution

It introduces a novel analysis of 4D simplicial gravity using geodesic distance and scaling relations, extending concepts from 2D loop distributions to 4D.

## Key findings

- Different scaling relations are identified in each coupling phase.
- Boundary volume distributions exhibit phase-dependent scaling behaviors.
- The study provides insights into the geometric properties of 4D quantum spacetime.

## Abstract

Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume distribution in 4D are discussed in various coupling regions i.e. strong-coupling phase, critical point and weak-coupling phase. In each phase the different scaling relations are found.