Duality of Coordinates and Matter Fields in Curved Spacetime

TL;DR

This paper explores a duality between local coordinates and matter field solutions in curved spacetime, revealing conditions under which this duality holds and discussing its implications for quantum theory.

Contribution

It establishes a specific duality between coordinates and Klein-Gordon solutions in curved spacetime, extending flat spacetime concepts with new constraints.

Findings

Duality exists under certain constraints in curved spacetime.

Derived equations governing the duality.

Discussed implications for quantum theory.

Abstract

We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the same generality as in flat spacetime and it holds only if the system satisfies certain constraints. We derive these constraints and the basic equations of duality and discuss the implications in the quantum theory.