Zero Values of the TOV Equation

TL;DR

This thesis explores the relativistic effects on the TOV equation by deriving an EoS for a non-interacting gas, presenting numerical solutions, and comparing zero values with the Lane-Emden equation, including new solutions and initial proof developments.

Contribution

It introduces a relativistic EoS for the TOV equation, compares its zero values with the Lane-Emden equation, and discovers new solutions and initial proof steps.

Findings

Zero values of TOV are smaller than those of LE for the same parameters.

Numerical solutions for various polytropic configurations are provided.

An exact solution and a new index n=2 solution of the LE equation are discovered.

Abstract

This thesis calculates the special-relativistic internal energy of a non-interacting gas. We derive an equation of state (EoS) which we apply to the Tollmann-Oppenheimer Volkoff (TOV) equation. Furthermore we present numerical results of the TOV equation for various configurations of a polytropic EoS. These results show that the zero values of the TOV equation compared to its non-relativistic counterpart, the Lane-Emden (LE) equation, are smaller for identical parameters. We present initial developments to a proof of this theorem. Furthermore, an additional exact solution and index $n=2$ of the LE equation was discovered.