Relativistic model for cold spherical interstellar gas clouds

TL;DR

This paper presents an exact relativistic model for cold spherical interstellar gas clouds, deriving metric functions, density profiles, and particle orbit stability consistent with recent astronomical data.

Contribution

It introduces a novel exact solution to Einstein's equations tailored for interstellar gas clouds, detailing their internal structure and particle dynamics.

Findings

Circular orbits are stable within the model.

The cloud exhibits rigid rotation with angular velocity inversely proportional to radius.

The model aligns with recent astronomical measurements.

Abstract

We investigate insterstellar gas spheres by determining the metric functions, the material distribution, and the features of particle orbits in terms of stability and geodesics. An exact solution of the Einstein's equations for interstellar gas clouds is derived that is compatible with the results of recent astronomical measurements. The solution determines the distribution of pressure and density, and it is suitable to describe the energy, speed, trajectory, and further relevant physical features of the cloud's particles. We describe the spacetime inside the nebula and give the density profile and the geodesics of particles. We find that circular orbits are stable and the cloud rotates rigidly by an angular velocity that is inversely proportional to the radius.