# Nonlinear Dynamics in the Einstein-Gauss-Bonnet gravity

## TL;DR

This study numerically explores how higher-order curvature corrections in Einstein-Gauss-Bonnet gravity influence nonlinear dynamics, singularity formation, and black hole thresholds in spherically and plane-symmetric spacetimes.

## Contribution

It provides new insights into the role of Gauss-Bonnet terms in nonlinear gravitational dynamics and singularity avoidance in higher-dimensional gravity models.

## Key findings

- Perturbed wormholes evolve into black holes or expanding throats based on energy and coupling constants.
- Large scalar pulse collisions produce high-curvature regions influenced by Gauss-Bonnet corrections.
- Positive Gauss-Bonnet corrections tend to prevent singularity formation, but do not eliminate it.

## Abstract

We numerically investigated how the nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms. We especially monitored the processes of appearances of a singularity (or black hole) in two models: (i) a perturbed wormhole throat in spherically symmetric space-time, and (ii) colliding scalar pulses in plane-symmetric space-time. We used a dual-null formulation for evolving the field equations, which enables us to locate the trapping horizons directly, and also enables us to follow close to the large-curvature region due to its causal integrating scheme. We observed that the fate of a perturbed wormhole is either a black hole or an expanding throat depending on the total energy of the structure, and its threshold depends on the coupling constant of the GB terms ($\alpha_{\rm GB}$). We also observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude also depends on $\alpha_{\rm GB}$. For both models, the normal corrections ($\alpha_{\rm GB}>0$) work for avoiding the appearance of singularity, although it is inevitable. We also found that in the critical situation for forming a black hole, the existence of the trapped region in the Einstein-GB gravity does not directly indicate the formation of a black hole.