Abstract
In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or overturning) for isotropic and anisotropic relativistic spheres. We show that a density profile rho (r), monotonous, decreasing and concave , i.e. rho ' < 0 and rho '' < 0, will be stable against convection, if the radial sound velocity monotonically decreases outward. We also studied the cracking instability scenarios and found that isotropic models can be unstable, when the reaction of the pressure gradient is neglected, i.e. delta mathcal {R}_p = 0; but if it is considered, the instabilities may vanish and this result is valid, for both isotropic and anisotropic matter distributions.
Highlights
The stability of general relativistic self-gravitating matter distributions has been extensively studied and reported in the literature through several techniques for many years. It is complex multivariate problem which depends on the micro-physics – bulk/shear viscosity, crust on the surface, magnetic field and so on – of the material constituents and their description through a macroscopic equation of state that characterizes the configuration
The cracking instability approach determines the tidal acceleration profiles generated by perturbations of the energy density and the anisotropy of pressures identifying the changes sign of the total force distribution within the system [20,21,22,23]. This approach has been applied to an anisotropic fluid with barotropic equations of state [24] and, more recently extended to take into account the perturbation of the pressure gradient in both isotropic and anisotropic matter configurations [25,26]
With this selection we study the effect of convective instability and the reaction of the pressure gradient to density perturbations
Summary
The stability of general relativistic self-gravitating matter distributions has been extensively studied and reported in the literature through several techniques for many years. The cracking instability approach determines the tidal acceleration profiles generated by perturbations of the energy density and the anisotropy of pressures identifying the changes sign of the total force distribution within the system [20,21,22,23]. This approach has been applied to an anisotropic fluid with barotropic equations of state [24] and, more recently extended to take into account the perturbation of the pressure gradient in both isotropic and anisotropic matter configurations [25,26].
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