A Geometrical Model for the Evolution of Spherical Planetary Nebulae Based on Thin-Shell Formalism

TL;DR

This paper presents a geometric thin-shell model for spherical planetary nebulae, deriving their evolution based on curvature tensors and energy-momentum considerations, providing a new theoretical framework for understanding their development.

Contribution

It introduces a novel geometrical model using thin-shell formalism to describe the evolution of spherical planetary nebulae, linking curvature tensors to nebula dynamics.

Findings

Derived expressions for energy density and pressure on the thin-shell.

Obtained the evolution pattern of the nebula radius over time.

Tested the model with a decreasing energy density function.

Abstract

A spherical planetary nebula is described as a geometric model. The nebula itself is considered as a thin-shell which visualized as a boundary of two spacetimes. The inner and outer curvature tensors of the thin-shell are found in order to get an expression of the energy-momentum tensor on the thin-shell. The energy density and pressure expressions are derived using the energy-momentum tensor. The time evolution of the radius of the thin-shell is obtained in terms of the energy density. The model is tested by using a simple power function for decreasing energy density and the evolution pattern of the planetary nebula is attained.