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 $$dM/d\rho _c >0$$dM/dρc>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.

We investigate the equilibrium and radial stability of spherically symmetric relativistic stars, considering a polytropic equation of state (EoS), within the framework of f(R,T) gravity with a conservative energy-momentum tensor. Both modified stellar structure equations and Chandrasekhar's pulsation equations are derived for the f(R,T)= R+ h(T) gravity model, where the function h(T) assumes a specific form in order to safeguard the conservation equation for the energy-momentum tensor. The neutron star properties, such as radius, mass, binding energy and oscillation spectrum are studied in detail. Our results show that a cusp — which signals the appearance of instability — is formed when the binding energy is plotted as a function of the compact star proper mass. We find that the squared frequency of the fundamental vibration mode passes through zero at the central-density value corresponding to such a cusp where the binding energy is a minimum.

In this work we study the properties of compact spheres made of a charged perfect fluid with a MIT bag model EoS for quark matter. Considering static spherically symmetric spacetime we derive the hydrostatic equilibrium equations in the recently formulated four dimensional Einstein–Gauss–Bonnet (4D EGB) gravity theory. In this setting, the modified TOV equations are solved numerically with the aim to investigate the impact of electric charge on the stellar structure. A nice feature of 4D EGB theory is that the Gauss–Bonnet term has a non-vanishing contribution to the gravitational dynamics in 4D spacetime. We therefore analyse the effects of Gauss–Bonnet coupling constant $$\alpha $$α and the charge fraction $$\beta $$β on the mass–radius ( $$M{-}R$$M - R ) diagram and also the mass–central density $$(M{-}\rho _c)$$( M - ρ c ) relation of quark stars. Finally, we conclude that depending on the choice of coupling constant one could have larger mass and radius compared with GR and can also be relevant for more massive compact objects due to the effect of the repulsive Coulomb force.

This study explores the behavior of compact stars within the framework of $$f(R,L_m,T)$$f ( R , L m , T ) gravity, focusing on the functional form $$f(R,L_m,T) = R + \alpha TL_m$$f ( R , L m , T ) = R + α T L m . The modified Tolman–Oppenheimer–Volkoff (TOV) equations are derived and numerically solved for several values of the free parameter $$\alpha $$α by considering both quark and hadronic matter—described by realistic equations of state (EoSs). Furthermore, the stellar structure equations are adapted for two different choices of the matter Lagrangian density (namely, $$L_m= p$$L m = p and $$L_m= -\rho $$L m = - ρ ), laying the groundwork for our numerical analysis. As expected, we recover the traditional TOV equations in General Relativity (GR) when $$\alpha \rightarrow 0$$α → 0 . Remarkably, we found that the two choices for $$L_m$$L m have appreciably different effects on the mass-radius diagrams. Results showcase the impact of $$\alpha $$α on compact star properties, while final remarks summarize key findings and discuss implications, including compatibility with observational data from NGC 6397’s neutron star. Overall, this research enhances comprehension of $$f(R,L_m,T)$$f ( R , L m , T ) gravity’s effects on compact star internal structures, offering insights for future investigations.

Within the metric formalism of f(R) theories of gravity, where R is the Ricci scalar, we study the hydrostatic equilibrium structure of compact stars with the inclusion of anisotropic pressure. In particular, we focus on the f(R) = R ^1+ϵ model and we examine small deviations from general relativity for |ϵ| ≪ 1. A suitable definition of mass function is explicitly formulated from the field equations and the value of the Ricci scalar at the center of each star is chosen such that it satisfies the asymptotic flatness requirement. We find that both the mass and the radius of a compact star are larger with respect to the general relativistic counterpart. Furthermore, we remark that the substantial changes due to anisotropy occur mainly in the high-central-density region.

We discuss the stability and construct dynamical configurations describing the gravitational collapse of unstable neutron stars with realistic equations of state compatible with the recent LIGO–Virgo constraints. Unlike other works that consider the collapse of a stellar configuration without a priori knowledge if it is stable or unstable, we first perform a complete analysis on stellar stability for such equations of state. Negative values of the squared frequency of the fundamental mode indicate us radial instability with respect to the collapse of the unstable star to a black hole. We find numerical solutions corresponding to the temporal and radial behaviour during the evolution of the collapse for certain relevant physical quantities such as mass, luminosity, energy density, pressure, heat flow, temperature, and quantities that describe bulk viscous processes. Our results show that the equation of state undergoes abrupt changes close to the moment of event horizon formation as a consequence of dissipative effects. During the collapse process all energy conditions are respected, which implies that our model is physically acceptable.