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The Hawking-Penrose (1970) singularity theorem weakens the causality assumption of global hyperbolicity used in the Penrose (1965) singularity theorem, at the expense of invoking the stronger timelike (instead of null) convergence condition…

Penrose's singularity theorem implies that if a trapped region forms in a gravitational collapse, then a singularity must form as well within such region. However, it is widely expected that singularities should be generically avoided by…

The essential singularity in Einstein's gravity can be avoidable if the preconditions of Penrose's theorem can be bypassed, i.e., if the strong energy condition is broken in the vicinity of a black hole center. The singularity mentioned…

The 1965 Penrose singularity theorem demonstrates the utterly inevitable and unavoidable formation of spacetime singularities under physically reasonable assumptions, and it remains one of the main results in our understanding of black…

The Penrose strong cosmic censorship conjecture asserts that Cauchy horizons inside dynamically formed black holes are unstable to remnant matter fields that fall into the black holes. The physical importance of this conjecture stems from…

An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from non-singular initial data. With standard assumptions about the spacetime, and assuming the existence of a trapped surface…

Is Cosmic Censorship special to General Relativity, or can it survive a violation of equivalence principle? Recent studies have shown that singularities in Lorentz violating Einstein-Aether (or Horava-Lifhsitz) theories can lie behind a…

In gravitational collapse leading to black hole formation, trapping horizons typically develop inside the contracting matter. Classically, an ingoing trapping horizon moves towards the centre where it reaches a curvature singularity, while…

Regular black holes represent a conservative model in which the classical singularity is replaced by a non-singular core without necessarily modifying the spacetime outside the trapping horizon. Given the possible lack of phenomenological…

A black hole is superentropic if it violates the reverse isoperimetric inequality. Recently, some studies have indicated that some four dimensional superentropic black holes have the null hypersurface caustics (NHC) outside their event…

Transforming Penrose's intuitive picture of a strong cosmic censorship principle, that generically forbids the appearance of locally naked space-time singularities, into a formal mathematical proof, remains at present, one of the most…

In spherical symmetry, solutions of the semiclassical Einstein equations belong to one of two possible classes. Both classes contain solutions that -- depending on the dynamic behavior of the horizon -- describe evaporating physical black…

We study the causal structure of dynamical charged black holes, with a sufficient number of massless fields, using numerical simulations. Neglecting Hawking radiation, the inner horizon is a null Cauchy horizon and a curvature singularity…

The classical Penrose inequality, a relation between the ADM mass and the area of any cross section of the black hole event horizon, was introduced as a test of the weak cosmic censorship conjecture: if it fails, the trapped surface is not…

The strong cosmic censorship conjecture, introduced by Penrose five decades ago, asserts that, in self-consistent theories of gravity, Cauchy horizons inside dynamically formed black holes should be unstable to remnant perturbation fields…

The Hawking-Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop…

The strong cosmic censorship conjecture (SCCC) proposed by Penrose states that the presence of the inner Cauchy horizon ($\mathcal{CH}$) in the black hole solutions does not threaten the deterministic nature of general relativity since it…

Regular black holes have become a popular alternative to the singular mathematical black holes predicted by general relativity as they circumvent mathematical pathologies associated with the singularity while preserving crucial black hole…

Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward, we investigate the non-linear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the…

Recently, several authors have studied the possibility of overspinning or overcharging an existing black hole to destroy its event horizon and make the central singularity naked. When all the effects are properly taken into account, any…