The Pressure Metric on the Margulis Multiverse

TL;DR

This paper introduces a pressure metric on the moduli space of Margulis spacetimes without cusps, proving its positive definiteness on constant entropy sections and establishing a key identity related to cross-ratio variations.

Contribution

It defines a new pressure metric on the Margulis multiverse and proves its positive definiteness and an important identity, advancing understanding of its geometric structure.

Findings

Pressure metric is positive definite on constant entropy sections.

An identity relating to the variation of cross-ratios is established.

Provides new insights into the geometry of Margulis spacetimes.

Abstract

This paper defines the pressure metric on the Moduli space of Margulis spacetimes without cusps and shows that it is positive definite on the constant entropy sections. It also demonstrates an identity regarding the variation of the cross-ratios.