Related papers: On the Penrose inequality
Under certain conditions, we give a new way to prove the uniqueness of static black hole in higher dimensional asymptotically flat spacetimes. In the proof, the Penrose inequality plays a key role in higher dimensions as well as four…
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…
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 proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in…
Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of…
The causal boundary construction of Geroch, Kronheimer, and Penrose has some universal properties of importance for general studies of spacetimes, particularly when equipped with a topology derived from the causal structure. Properties of…
In 1979 Penrose hypothesized that the arrows of time are explained by the hypothesis that the fundamental laws are time irreversible. That is, our reversible laws, such as the standard model and general relativity are effective, and emerge…
We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied…
A Penrose diagram is constructed for a spatially coherent black hole that smoothly begins an accretion, then excretes symmetrically as measured by a distant observer, with the initial and final states described by a metric of Minkowski…
In the traditional formalism of quantum mechanics, a simple direct proof of (a version of) the Spin Geometry Theorem of Penrose is given; and the structure of a model of the `space of the quantum directions', defined in terms of elementary…
In this two-part paper, we review, and then develop, the assessment of the hole argument for general relativity. This first Part reviews the literature hitherto, focussing on the philosophical aspects. It also introduces two main ideas we…
In this paper, we introduce a new family of mass-type invariants for time-symmetric initial data in space-times satisfying the Dominant Energy Condition. For positive cosmological constant, these invariants, unlike the total Hawking mass,…
In this short note we explain how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8.
Inspired by the proof of the Bertrand postulate given by P. Erd\H{o}S, we carefully examine and solve one less usual inequality in positive integers which could help to find an arithmetically pure proof that for every positive integer…
We investigate the magnetic Penrose process in the Quevedo-Mashhoon spacetime, immersed in a uniform magnetic field $B$. This metric is a stationary, axisymmetric, asymptotically flat vacuum solution to Einstein's equations with an…
As an interesting application of the Einstein-Gauss-Bonnet theory and our work on the Gauss-Bonnet-Chern mass (Ge, Wang, Wu), we obtain a positive mass theorem for asymptotically flat graphs in $\R^{n+1}$ under a condition that $R+\alpha…
The main result of this paper supports a conjecture by C. P\'erez and E. Rela about a very recent result of theirs on self-improving theory. Also, we extend the conclusions of their theorem to the range $p<1$. As an application of our…
We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM energy-momentum vector $(E,P)$ of the…
This article reviews a recent work by a couple of colleagues and myself about the shortcomings of the standard explanations of the quantum origin of cosmic structure in the inflationary scenario, and a proposal to address them. The point it…
It is the purpose of the present article to collect arguments for, that there should exist in fact -- although not necessarily yet found -- some law, which imply an adjustment to special features to occur in the future. In our own "complex…