# Complexity of the Bondi metric

## TL;DR

This paper extends a complexity concept to vacuum solutions in relativity, establishing a hierarchy from simple Minkowski spacetime to radiating systems, and differentiates between types of non-radiative systems based on their complexity.

## Contribution

It introduces a complexity hierarchy for vacuum solutions in relativity and distinguishes between natural and non-natural non-radiative systems.

## Key findings

- Minkowski spacetime is the simplest in the hierarchy.
- Radiating systems are more complex than non-radiative ones.
- Non-natural non-radiative systems are identified as simpler than natural non-radiative systems.

## Abstract

A recently introduced concept of complexity for relativistic fluids is extended to the vacuum solutions represented by the Bondi metric. A complexity hierarchy is established, ranging from the Minkowski spacetime (the simplest one) to gravitationally radiating systems (the more complex). Particularly interesting is the possibility to differentiate between natural non--radiative (NNRS) and non--natural non--radiative (NNNRS) systems, the latter appearing to be simpler than the former. The relationship between vorticity and the degree of complexity is stressed.