We investigate here the locally naked singularity formed due to a spherically symmetric inhomogeneous collapsing cloud having nonzero isotropic pressure, in terms of its strength. A sufficient condition provided by Clarke and Krolak for it to be Tipler strong has been used to restrict the parameters that represent the nonlinear relation between the physical radius and the radial coordinate of the outgoing radial null geodesic at the singular center. Studying an end state of a collapsing cloud requires information about the dynamics of collapse, which is unknown in a general scenario. Hence we study small perturbations to the mass profile for inhomogeneous dust, which is possible using the formalism developed here. This perturbed mass profile, in turn, gives rise to nonzero pressure. We show the existence of a nonzero measure set of initial data giving rise to such strong curvature naked singularity.

We investigate here the local versus global visibility of a spacetime singularity formed due to the gravitational collapse of a spherically symmetric dust cloud having a nonzero velocity function. The conditions are investigated that ensure the global visibility of the singularity, in the sense that the outgoing null geodesics leave the boundary of the matter cloud in the future, whereas, in the past, these terminate at the singularity. Explicit examples of this effect are constructed. We require that this must be a strong curvature singularity in the sense of Tipler, to ensure the physical significance of the scenario considered. This may act as a counterexample to the weak cosmic censorship hypothesis.

We investigate here the final state of gravitational collapse of a non-spherical and non-marginally bound dust cloud as modeled by the Szekeres spacetime. We show that a directionally globally naked singularity can be formed in this case near the collapsing cloud boundary and not at its geometric center, as is typically the case for a spherical gravitational collapse. This singularity is a strong curvature naked singularity in the sense of Tipler criterion on gravitational strength. The null geodesics escaping from the singularity would be less scattered in this case in certain directions since the singularity is close to the boundary of the cloud, as is the case in the current scenario. The physical implications are pointed out.

The global visibility of a singularity as an end state of the gravitational collapse of a spherically symmetric pressureless cloud is investigated. We show the existence of a non-zero measured set of parameters: the total mass and the initial mean density of the collapsing cloud, giving rise to a physically strong globally visible singularity as the end state for a fixed velocity function. The existence of such a set indicates that such singularity is stable under small perturbation in the initial data causing its existence. This is true for marginally as well as non-marginally bound cases. The possibility of the presence of such suitable parameters in the astrophysical setup is then studied: (1) The singularities’ requirements at the centre of the M87 galaxy and at the centre of our galaxy (SgrA*) to be globally visible are discussed in terms of the initial size of the collapsing cloud forming them, presuming that such singularities are formed due to gravitational collapse. (2) The requirement for the primordial singularities formed due to a collapsing configuration after getting detached from the background universe at the time of matter-dominated era just after the time of matter-radiation equality, to be globally visible, is discussed. (3) The scenario of the collapse of a neutron star after reaching a critical mass, which is achieved by accreting the supernova ejecta expelled by its binary companion core progenitor, is considered. The primary aim of this paper is to show that globally visible singularities can form in astrophysical setups under appropriate circumstances.

We study here the unhindered gravitational collapse of spatially homogeneous (SH) scalar fields $\varphi$ with a potential $V_s(\varphi )$, as well as vector fields $\tilde{A}$ with a potential $V_v(B)$ where $B=g(\tilde{A},\tilde{A})$ and $g$ is the metric tensor. We show that in both cases, classes of potentials exist that give rise to black holes or naked singularities. The strength of the naked singularity when it occurs is examined, and these are found to be gravitationally strong in the sense of Tipler, for a wide class of respective potentials (for both scalar and vector fields). We match the collapsing scalar or vector field with a generalized Vaidya spacetime outside. We highlight that full generality is maintained within the domain of SH scalar or vector field collapse.