Adiabatic stability of stellar models in the unimodular framework

Sudan Hansraj; Njabulo Mkhize

doi:10.1140/epjp/i2019-12637-7

EPJ

Adiabatic stability of stellar models in the unimodular framework

Sudan Hansraj¹^* and Njabulo Mkhize²

¹ Astrophysics and Cosmology Research Unit, University of KwaZulu Natal, Durban, South Africa
² University of KwaZulu Natal, Durban, South Africa

Received: 14 November 2018
Accepted: 24 December 2018
Published online: 2 April 2019

Abstract

We investigate the behaviour of the Tolman metrics within the formalism of the trace-free (or unimodular) gravity. A solution generating algorithm is presented which influences the physical character of the models proposed. Specifically an additive constant of integration (K) is persistently in attendance and while it has little influence on the density, pressure, energy conditions and sound speed it exerts considerable influence on the equation of state, active gravitational mass and hence the compactification parameter (mass-to-radius ratio) as well as on the Chandrasekhar adiabatic stability index. A thorough study of the Tolman IV and V metrics is conducted and it is evident that the adiabatic stability criterion $\frac{\rho + p}{p} \frac{\mathrm{d}p}{\mathrm{d}\rho} > \frac{4}{3}$ is achievable in the presence of K but not without at least in the Tolman IV case. A range of parameter values for the Tolman V solution is considered and graphical plots corroborate that the Tolman choice $n = \frac{1}{2}$ only allows for the model’s compatibility with the elementary requirements for physical plausibility.

12 Internat. Congress of the Balkan Physical Union
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EPJ

Adiabatic stability of stellar models in the unimodular framework

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