# Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaitre-Robertson-Walker spacetimes: Stability and isoperimetric inequalities

## TL;DR

This paper studies toroidal marginally outer trapped surfaces in closed FLRW spacetimes, analyzing their stability and isoperimetric properties by embedding CMC Clifford tori, and finds they are generally unstable.

## Contribution

It introduces a method to construct toroidal MOTS in FLRW spacetimes and evaluates their stability and isoperimetric inequalities, extending previous symmetric cases.

## Key findings

- Toroidal MOTS are constructed via CMC Clifford tori.
- These toroidal MOTS are found to be unstable.
- The study assesses isoperimetric inequalities in this context.

## Abstract

We investigate toroidal Marginally Outer Trapped Surfaces (MOTS) and Marginally Outer Trapped Tubes (MOTT) in closed Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. They are constructed by embedding Constant Mean Curvature (CMC) Clifford tori in a FLRW spacetime. This construction is used to assess the quality of certain isoperimetric inequalities, recently proved in axial symmetry. Similarly to spherically symmetric MOTS existing in FLRW spacetimes, the toroidal ones are also unstable.