Fractional Boundaries for Fluid Spheres

TL;DR

This paper introduces a fractional derivative matching method to generate a family of Israel layers between two metrics, expanding modeling options for fluid spheres and analyzing their physical properties.

Contribution

It presents a novel fractional derivative approach to create a continuum of boundary layers between metrics, enhancing fluid sphere modeling capabilities.

Findings

Creates new parameter ranges for fluid sphere models.

Applies method to Tolman and Schwarzschild metrics.

Clarifies pressure and tension in boundary layers.

Abstract

A single Israel layer can be created when two metrics adjoin with no continuous metric derivative across the boundary. The properties of the layer depend only on the two metrics it separates. By using a fractional derivative match, a family of Israel layers can be created between the same two metrics. The family is indexed by the order of the fractional derivative. The method is applied to Tolman IV and V interiors and a Schwarzschild vacuum exterior. The method creates new ranges of modeling parameters for fluid spheres. A thin shell analysis clarifies pressure/tension in the family of boundary layers.