Novel Geometrical Models of Relativistic Stars. II. Incompressible Stars and Heavy Black Dwarfs

TL;DR

This paper introduces a new class of geometrical models for relativistic stars, demonstrating the existence of heavy black dwarfs with large mass but small radius and luminosity, supported by mathematical proofs and analysis of incompressible star solutions.

Contribution

It provides a mathematical proof of heavy black dwarfs and explores the entire solution space of incompressible relativistic stars within a novel geometrical framework.

Findings

Existence of heavy black dwarfs with arbitrary mass and small radius.

Complete solution analysis of incompressible star models.

Discussion of observational data relevance.

Abstract

In a series of articles we describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge conditions. It turns out that there exist heavy black dwarfs: relativistic stars with arbitrary large mass, which are to have arbitrary small radius and arbitrary small luminosity. In the present article we mathematically prove this new phenomena, using a detailed consideration of incompressible GR stars. We study the whole two parameter family of solutions of extended TOV equations for incompressible stars. This example is used to illustrate most of the basic features of the new geometrical models of relativistic stars. Comparison with newest observational data is discussed