Adiabatic stability of stellar models in the unimodular framework

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.