Dynamical deformation of 2+1 dimensional double torus universe

TL;DR

This paper investigates the dynamics of a double torus universe in (2+1)-dimensional gravity, focusing on affine deformations and their mathematical formulation using holomorphic quadratic differentials.

Contribution

It introduces a detailed formulation of the Einstein-Hilbert action for affine stretching parameters and provides a concrete solution for the dynamics along a holomorphic quadratic differential.

Findings

Explicit description of affine stretching modes

Formulation of Einstein-Hilbert action for deformation parameters

Concrete solution for the dynamics along quadratic differentials

Abstract

In (2+1)-dimensional pure gravity with cosmological constant, the dynamics of double torus universe with pinching parameter is investigated. Each mode of affine stretching deformation is illustrated in the context of horizontal foliation along the holomorphic quadratic differential. The formulation of the Einstein Hilbert action for the parameters of the affine stretching is developed. Then the dynamics along one holomorphic quadratic differential will be solved concretely.