Related papers: Present status of the Penrose inequality
In this essay I first discuss the physical relevance of the inequality $m\geq \sqrt{|J|}$ for axially symmetric (non-stationary) black holes, where m is the mass and J the angular momentum of the spacetime. Then, I present a proof of this…
In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have…
This is the second in a series of two papers to establish the conjectured mass-angular momentum inequality for multiple black holes, modulo the extreme black hole 'no hair theorem'. More precisely it is shown that either there is a…
Black hole physics currently lacks a fully coherent understanding of the black hole mass (density), entropy, and interior (non-)singularity. These concepts are related to the black hole radius, area (of the horizon), and volume (within the…
We explore the extraction of energy from a rotating black hole spacetime modified by a quantum correction parameter \( \alpha \). Focusing on particle splitting within the ergoregion, we analyze the Penrose process and compute the…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity…
A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several…
We present two alternative perspectives for the resolution of Hawking's information puzzle in black hole evaporation. The two views are deeply contrasting, yet they share several common aspects. One of them is the central role played by the…
Addressing the general question whether Penrose singularities physically exist inside black holes, we investigate the problem in the context of an analogue system, a flowing laboratory liquid, for which the governing equations are at least…
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…
The main goal of this paper is to present a series of inequalities connecting the surface area measure of a convex body and surface area measure of its projections and sections. We present a solution of a question from S. Campi, P.…
This is a review of my work published in the papers [1-4]. It offers a more detailed discussion of the results than what was given in the published papers and it links my results to some conclusions recently made by other people. It also…
The Robinson-Trautman space-times provide solutions of Einstein's equations with negative cosmological constant, which settle to $AdS_4$ Schwarzschild black hole at late times. Via gauge/gravity duality they should describe a system out of…
A Penrose diagram is constructed for a spatially coherent black hole that accretes at stepwise steady rates as measured by a distant observer from an initial state described by a metric of Minkowski form. Coordinate lines are…
We prove a sharp Alexandrov-Fenchel-type inequality for star-shaped, strictly mean convex hypersurfaces in hyperbolic $n$-space, $n\geq 3$. The argument uses two new monotone quantities along the inverse mean curvature flow. As an…
Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of…
Infalling matter may destroy a black hole and expose the naked singularity. Thus, Penrose proposed the weak cosmic censorship conjecture to avoid such a possibility. On the other hand, if the black hole is not destroyed by infalling matter,…
We show that the Penrose inequality is satisfied for a class of conformally flat axially symmetric nonmaximal perturbations of the Schwarzschild data. A role of horizon is played by a marginally outer trapped surface which does not have to…
We investigate the weak cosmic censorship conjecture in Myers-Perry black holes with arbitrary rotations in general dimensions based on the scattering of a massless scalar field. From the fluxes of the scalar field flowing into the black…