Natural Coordinate System in Curved Space-time

TL;DR

This paper introduces a natural coordinate system in curved space-time that is globally valid, aligns with physical evolution, and simplifies the expression of physical laws, aiding in understanding space-time's nature.

Contribution

It proposes a new natural coordinate system in curved space-time with a concrete construction method and discusses its physical and geometrical significance.

Findings

Simplifies the expression of physical laws in curved space-time

Facilitates classical and Newtonian approximations in curved space-time

Helps in understanding the nature of space-time through examples

Abstract

In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving process and keep synchronous with the evolution of the realistic world. In this coordinate system, it is convenient to express the physical laws and to calculate physical variables with clear geometrical meaning. We call it "natural coordinate system". The constructing method for the natural coordinate system is concretely provided, and its physical and geometrical meanings are discussed in detail. In NCS we make classical approximation of spinor equation to get Newtonian mechanics, and then make weak field approximation of Einstein's equation and low speed approximation of particles moving in the space-time. From the analysis and examples we find it is a nice coordinate system to describe the realistic curved space-time, and is helpful to understand the nature of space-time.