Nonlinear phenomena in general relativity

TL;DR

This paper explores nonlinear phenomena in general relativity, focusing on horizon formation and the importance of higher-order perturbations to accurately describe effects like the cosmological constant.

Contribution

It demonstrates the necessity of second-order perturbation theory to capture horizon formation and cosmological constant effects in general relativity.

Findings

Lower order perturbations cannot describe horizon formation.

Second-order expansion is required to include cosmological constant effects.

Higher-order perturbations are essential for accurate modeling of nonlinear phenomena.

Abstract

The perturbation theory plays an important role in studying structure formation in cosmology and post-Newtonian physics, but not all phenomena can be described by the linear perturbation theory. Thus, It is necessary to study exact solutions or higher order perturbations. Specifically, we study black hole (apparent) horizons and the cosmological event horizon formation in the perturbation theory. We emphasize that in the perturbative regime of the gravitational potential these horizons cannot form in the lower order. Studying the infinite plane metric, we show that to capture the cosmological constant effect we need at least a second order expansion.