Recognizable classification of Lorentzian distance-squared mappings

TL;DR

This paper classifies Lorentzian distance-squared mappings based on recognition subspaces, providing a comprehensive understanding of their structure in Lorentzian geometry.

Contribution

It introduces a natural extension of Lorentzian distance-squared functions and offers a complete classification based on recognition subspaces.

Findings

Complete classification of Lorentzian distance-squared mappings

Identification of recognition subspaces as key classification criteria

Framework for analyzing Lorentzian geometric functions

Abstract

The Lorentzian length, which is one of the most significant functions in Lorentzian geometry, is a complex-valued function. Its square gives a real-valued non-degenerate quadratic function. In this paper, we define naturally extended mappings of Lorentzian distance-squared functions, wherein each component is a Lorentzian distance-squared function; and classify these mappings completely by the likeness of recognition subspaces.