Differential Structure of Space-Time and Physical Fields

TL;DR

This paper interprets the differential structure of space-time physically, exploring its implications for cosmic strings with scalar fields, revealing that smoothness assumptions lead to modified global properties or quantized deficit angles.

Contribution

It introduces a physical interpretation of space-time axioms and demonstrates their consequences for cosmic string space-times with scalar fields, including quantization effects.

Findings

Quantization of the deficit angle in cosmic string space-times

Modification of global properties due to scalar field smoothness

Physical interpretation of differential structure axioms

Abstract

A physical interpretation of axioms of the differential structure of space-time is presented. Consequences of such interpretation for cosmic string's space-time with a scalar field are studied. It is shown that the assumption of smoothness of the scalar field leads either to modification of cosmic string's space-time global properties or to quantization of the deficit of angle: $\Delta =2\pi (1-1/n)$, $n=1,2,\dots$.