Causal structure of singularity in non-spherical gravitational collapse

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

On the visibility of singularities in general relativity and modified gravity theories

We argue that the global causal structure of the singularity is not a purely geometric property but also depends on the collapsing matter-field leading to its formation. To show this, we investigate the global visibility of the end state of a spherically symmetric marginally bound Lemaitre-Tolman-Bondi collapsing cloud (which is well studied in general relativity) in the framework of modified gravity having the generalized Lagrangian $R+\alpha R^2$ in the Einstein-Hilbert action. Here $R$ is the Ricci scalar, and $\alpha>0$ is a constant. As an example, we depict that for the same LTB metric governing the spacetime formed due to two different matter-fields, i.e., dust in general relativity and imperfect viscous fluid in $f(R)$ gravity, the singularity is locally visible in the former case, and globally visible in the latter case.Comment: 10 pages, 4 figure