Related papers: Present status of the Penrose inequality

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…

Motivated by the rigidity case in the localized Riemannian Penrose inequality, we show that suitable singular metrics attaining the optimal value in the Riemannian Penrose inequality is necessarily smooth in properly specified coordinates.…

The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a…

We identify a condition on spacelike 2-surfaces in a spacetime that is relevant to understanding the concept of mass in general relativity. We prove a formula for the variation of the spacetime Hawking mass under a uniformly area expanding…

Penrose et al. investigated the physical incoherence of the spacetime with negative mass via the bending of light. Precise estimates of time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we…

In this paper we investigate the extension of the charged Riemannian Penrose inequality to the case where charges are present outside the horizon. We prove a positive result when the charge densities are compactly supported, and present a…

Of the various energy conditions which can be assumed when studying mathematical general relativity, intuitively the simplest is the weak energy condition $\mu\geq 0$ which simply states that the observed mass-energy density must be…

After a detailed introduction including new examples, we give an exposition focusing on the Riemannian cases of the positive mass, Penrose, and ZAS in- equalities of general relativity, in general dimension.

We propose a new notion of singularity in General Relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a spacetime has a volume singularity if there exist points…

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"…

Penrose described a process that, in principle, could extract energy and angular momentum from a rotating black hole. Here we examine two procedures that were claimed to be capable of implementing the Penrose idea; both make use of a…

A Penrose diagram is constructed for an example black hole that evaporates at a steady rate as measured by a distant observer, until the mass vanishes, yielding a final state Minkowski space-time. Coordinate dependencies of significant…

We prove that the Riemannian Penrose Inequality holds for Asymptotically Flat $3$-manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the $\mathrm{ADM}$…

The singularity theorems of Hawking and Penrose tell us that singularities are common place in general relativity. Singularities not only occur at the beginning of the Universe at the Big Bang, but also in complete gravitational collapses…

We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important…

Penrose's weak cosmic censorship conjecture asserts that spacetime singularities produced by gravitational collapse are generically hidden behind event horizons, thus preventing them from causally influencing distant observers and…

We prove the Riemannian Penrose inequality in arbitrary dimension for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing minimal boundary, where the boundary is allowed to have a…

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…

Penrose's crucial contributions to General Relativity, symbolized by his 1965 singularity theorem, received (half of) the 2020 Nobel prize in Physics. A renewed interest in the ideas and implications behind that theorem, its later…

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…