# Challenges to global solutions in Horndeski's theory

## TL;DR

This paper investigates the conditions and obstacles for obtaining global solutions in Horndeski's gravity theories, using the Einstein frame and numerical simulations to analyze the problem.

## Contribution

It provides a systematic analysis of global solutions in Horndeski's theories and identifies key conditions and challenges for their existence.

## Key findings

- Conditions for global solutions are identified.
- Obstacles to global solutions are characterized.
- Numerical simulations illustrate potential issues.

## Abstract

We explore the question of obtaining global solutions in Horndeski's theories of gravity. Towards this end, we study a relevant set of the theory and, by employing the Einstein frame we simplify the analysis by exploiting known results on global solutions of wave equations. We identify conditions for achieving global solutions as well as obstacles that can arise to spoil such goal. We illustrate such problems via numerical simulations.