Unstable Anisotropic Neutron Stars: Probing the Limits of Gravitational Collapse

Neutron stars (NSs) are incredibly versatile for studying various important aspects of high-energy and compact-object physics. These celestial objects contain extreme matter at incredibly high densities in their interiors, leading to the risk of instabilities that may cause them to collapse into a black hole (BH). This paper focuses on exploring the stability and gravitational collapse of NSs. For a more realistic approach we have considered the pressure to be locally anisotropic. We utilize the BL-Model to describe the anisotropy inside the NS. The presence of quarks in the core of an NS can heavily affect its stability. Hence, along with pure hadronic EOSs, we have also considered Hadron-Quark phase transition (HQPT) EOSs for this paper's analysis. We subject the anisotropic NSs to radial perturbations to study their stability against radial oscillations. NSs exhibiting imaginary eigen-frequencies are identified as unstable, and their inevitable destiny is gravitational collapse, resulting in the formation of a BH. We consider the interior of these unstable anisotropic NSs to be a non-ideal fluid in a non-adiabatic background in order to study its dynamical evolution during the collapse. We examine the temporal evolution of key properties of NSs, such as mass, density, heat flux, and anisotropy during the process of gravitational collapse. We present an innovative and viable approach to detect such high-energy gravitational collapse events, providing valuable insights into the properties of the static NS before its collapse.