Related papers: Penrose's singularity theorem and the Kerr space-t…

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…

The singularity theorems of Penrose, Hawking, and Geroch predict the existence of incomplete inextendible causal geodesics in a wide range of physically adequate spacetimes modeling the gravitational collapse of stars and the expanding…

In this paper, we study rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces…

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…

We present a review of the two prominent singularity theorems due to Penrose and Hawking, as well as their physical interpretation. Their usage is discussed in detail for the Schwarzschild spacetime with positive and negative mass. First,…

We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to…

We consider versions of the Penrose singularity theorem and the Hawking horizon topology theorem in weighted spacetimes that contain weighted versions of trapped surfaces, for arbitrary spacetime dimension and synthetic dimension. We find…

The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penrose's…

We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity $C^{1,1}$. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.

I argue that spacetime singularities entail no ontological commitment to material entities. First, I show that Penrose's singularity theorem is best understood as a theorem of incompleteness, it demonstrates the failure of specific…

Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose's original singularity theorem, it implies that spacetime is null geodesically…

We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u^{-2}-behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic…

The 2020 Nobel prize in Physics has revived the interest in the singularity theorems and, in particular, in the Penrose theorem published in 1965. In this short paper I briefly review the main ideas behind the theorems and then proceed to…

Penrose's original heuristic for his eponymous spacetime inequality -- a conjectured lower bound on the ADM mass in terms of the area of a horizon cross-section -- relies on the black hole final state conjecture. In this paper we isolate a…

The classical singularity theorems of R. Penrose and S. Hawking from the 1960s show that, given a pointwise energy condition (and some causality as well as initial assumptions), spacetimes cannot be geodesically complete. Despite their…

Supplementing earlier literature by e.g. Tipler, Clarke, & Ellis (1980), Israel (1987), Thorne, (1994), Earman (1999), Senovilla & Garfinkle (2015), Curiel (2019ab), and Landsman (2021ab), I provide a historical and conceptual analysis of…

Assuming the Bousso bound, we prove a singularity theorem: if the light rays entering a hyperentropic region contract, then at least one light ray must be incomplete. "Hyperentropic" means that the entropy of the region exceeds the…

What happens at spacetime singularities is poorly understood. The Penrose-Wall singularity theorem constrains possible scenarios, but until recently its key assumption--the generalized second law (GSL)--had only been proven perturbatively,…

We show that a globally hyperbolic spacetime containing a trapped surface and satisfying the strong energy condition and a condition on certain radial tidal forces must be timelike geodesically incomplete. This constitutes a "timelike"…