# Linking Past and Future Null Infinity in Three Dimensions

## TL;DR

This paper establishes a symmetry-based mapping between past and future null infinity in 3D flat space, revealing energy-preserving properties and an infinite set of conservation laws in asymptotic symmetries.

## Contribution

It introduces a novel mapping between past and future null infinity in three dimensions, connecting their asymptotic symmetry groups.

## Key findings

- Mapping is energy preserving
- Infinite conservation laws derived
- Asymptotic symmetry groups are related

## Abstract

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.