Abstract
In this work we construct families of anisotropic neutron stars for an equation of state compatible with the constraints of the gravitational-wave event GW170817 and for four anisotropy ansatze. Such stars are subjected to a radial perturbation in order to study their stability against radial oscillations and we develop a dynamical model to describe the non-adiabatic gravitational collapse of the unstable anisotropic configurations whose ultimate fate is the formation of a black hole. We find that the standard criterion for radial stability dM/drho _c >0 is not always compatible with the calculation of the oscillation frequencies for some anisotropy ansatze, and each anisotropy parameter is constrained taking into account the recent restriction of maximum mass of neutron stars. We further generalize the TOV equations within a non-adiabatic context and we investigate the dynamical behaviour of the equation of state, heat flux, anisotropy factor and mass function as an unstable anisotropic star collapses. After obtaining the evolution equations we recover, as a static limit, the background equations.
Highlights
The most common matter-energy distribution for modeling the internal structure of compact stars is an isotropic perfect fluid
We are interested in considering a realistic equation of state (EoS), which is compatible with the restriction obtained from this merger, and exploring the effects it can have on the physical characteristics of stable and unstable anisotropic stars
We have carried out an analysis of adiabatic radial pulsations for such stars in order to study their radial stability against gravitational collapse
Summary
The most common matter-energy distribution for modeling the internal structure of compact stars is an isotropic perfect fluid. A conventional technique widely used to indicate the onset of instability is the M(ρc) method [17], known as a necessary condition for stability analysis of compact stars [29,30] This boundary between the stable and unstable stars describes the maximum amount of mass that can exist in a configuration before it must undergo a gravitational collapse. In addition to generating hydrostatically stable anisotropic configurations, we are interested in studying the process of gravitational collapse of the unstable configurations In this regard, the pioneering work about gravitational collapse for a spherically symmetric distribution of matter in the form of dust cloud was carried out by Oppenheimer and Snyder [54]. We adopt the signature (−, +, +, +) and physical units will be used throughout this work
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