# Gravitational geons in asymptotically anti-de Sitter spacetimes

## TL;DR

This paper presents the first numerical constructions of fully non-linear gravitational geons in four-dimensional asymptotically anti-de Sitter spacetimes, reaching high amplitudes and confirming the existence of excited geon solutions.

## Contribution

The study introduces a novel numerical approach to construct non-linear geons in AdS, including excited states, with high amplitude and precision, expanding understanding of gravitational solitons.

## Key findings

- Successfully constructed multiple geon families seeded by spherical harmonics.
- Achieved high amplitudes with mass around half the AdS length.
- Provided strong numerical evidence for excited geon solutions.

## Abstract

We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3+1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order $\sim 1/2$ of the AdS length, and with deviations of the order of 50\% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities like mass and angular momentum are computed using two independent frameworks that agree each other at the $0.1\%$ level. We also provide strong evidence for the existence of excited (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.