arXiv research

Proves weak cosmic censorship for a specific Einstein-scalar field system in 2+1 dimensions.

Proves inextendibility of weak null singularities from curvature blow-up.

The study proves strong cosmic censorship violation for spherically symmetric dust clouds.

Penrose's conjecture links black holes and gravitational singularities.

Proof confirms cosmic censorship for charged gravitational collapse.

Study on naked singularities without symmetry, forming incomplete future null infinity and singular inner Cauchy horizon.

Proposes a weaker version of Strong Cosmic Censorship with curvature bounds.

This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the sign of the curvature $k$ of the symmetric surfaces and the cosmological constant $…

For almost half of the one hundred year history of Einstein's theory of general relativity, Strong Cosmic Censorship has been one of its most intriguing conjectures. The SCC conjecture addresses the issue of the nature of the singularities found in most solutions of Einstein's gravitational field equations: Are such si…

New data shows multiple black holes can form from modified vacuum data.

We address the issue of strong cosmic censorship for T^2-symmetric spacetimes with positive cosmological constant. In the case of collisionless matter, we complete the proof of the C^2 formulation of the conjecture for this class of spacetimes. In the vacuum case, we prove that the conjecture holds for the special case…

We initiate the mathematical study of spherical collapse of self-gravitating charged scalar fields. The main result gives a complete characterization of the future boundary of spacetime, providing a starting point for studying the cosmic censorship conjectures. In general, the boundary includes two null components, one…

Proves conditions for Cauchy horizons in low-regularity spacetimes.

We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the exp…

New singularity concept in GR: volume singularities.

Study on black hole interiors with matter fields, showing oscillation condition impacts blow-up.

The paper connects Diophantine approximation to black hole behavior, proving blow-up conditions.

The paper examines gravitational singularities in spacetimes and proves inextendibility.

We study Jang's equation on a one-parameter family of asymptotically flat, spherically symmetric Cauchy hypersurfaces in the maximally extended Schwarzschild spacetime. The hypersurfaces contain apparent horizons and are parametrized by their proximity to the singularity at $r = 0$. We show that on those hypersurfaces …

Proves existence of Killing fields in smooth spacetimes with compact Cauchy horizons.

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the produc…

The Strong Cosmic Censorship conjecture states that for generic initial data to Einstein's field equations, the maximal globally hyperbolic development is inextendible. We prove this conjecture in the class of orthogonal Bianchi class B perfect fluids and vacuum spacetimes, by showing that unboundedness of certain curv…

In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of this result in the contexts of cosmic censorship and the initial value problem i…

The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic spacetimes, (2) the relativistic initial value problem, (3) constant mean curvat…

Motivated by the cosmic censorship conjecture in mathematical relativity, we establish the precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. In particular this result does not require the res…

Study shows instability of naked singularities in scalar field models.

In this letter a generic counterexample to the strong cosmic censor conjecture is exhibited. More precisely---taking into account that the conjecture lacks any precise formulation yet---first we make sense of what one would mean by a "generic counterexample" by introducing the mathematically unambigous and logically st…

Constructs initial data leading to apparent horizons and tests Penrose Inequality.

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that it is even inextendible as a Lorentzian manifold with a continuous metric. To capture the obstruction to continuous extens…

We use the inverse mean curvature flow to establish Penrose-type inequalities for time-symmetric Einstein-Maxwell initial data sets which can be suitably embedded as a hypersurface in Euclidean space $\mathbb R^{n+1}$, $n\geq 3$. In particular, we prove a positive mass theorem for this class of charged black holes. As …

The positive mass theorem is one of the fundamental results in general relativity. It states that, assuming the dominant energy condition, the total mass of an asymptotically flat spacetime is non-negative. The Penrose inequality provides a lower bound on mass by the area of the black hole and is closely related to the…

New model reduces bias in cosmic shear measurements.

We note an area-charge inequality orignially due to Gibbons: if the outermost horizon $S$ in an asymptotically flat electrovacuum initial data set is connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4π}$ is the area radius of $S$. A consequence of this inequality is that for connected black hole…

Let $M$ be a connected, simply connected, oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put $M^\times:=M\setminus\{{\rm point}\}$.In this paper we prove that if $X^\times$ is a smooth four-manifold homeomorphic but not necessarily diffeomorphic to $M^\times$ (m…

We consider the wave equation on Reissner-Nordström-de Sitter and more generally Kerr-Newman-de Sitter black hole spacetimes with $Λ>0$. The strength of the blue-shift instability associated to the Cauchy horizon of these spacetimes has been the subject of much discussion, since-in contrast to the $Λ=0$ case-the compet…

Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical sym…

In our previous article [Rad16], we investigated the asymptotic behaviour of orthogonal Bianchi class B perfect fluids close to the initial singularity and proved the Strong Cosmic Censorship conjecture in this setting. In several of the statements, the case of a stiff fluid had to be excluded. The present paper fills …

We prove that a large class of smooth solutions $ψ$ to the linear wave equation $\Box_gψ=0$ on subextremal rotating Kerr spacetimes which are regular and decaying along the event horizon become singular at the Cauchy horizon. More precisely, we show that assuming appropriate upper and lower bounds on the energy along t…

Motivated by the Strong Cosmic Censorship Conjecture for asymptotically AdS spacetimes, we initiate the study of massive scalar waves satisfying $\Box_g ψ- μψ=0$ on the interior of Anti-de Sitter (AdS) black holes. We prescribe initial data on a spacelike hypersurface of a Reissner--Nordström--AdS black hole and impose…

The Penrose inequality gives a lower bound for the total mass of a spacetime in terms of the area of suitable surfaces that represent black holes. Its validity is supported by the cosmic censorship conjecture and therefore its proof (or disproof) is an important problem in relation with gravitational collapse. The Penr…

The existence, established over the past number of years and supporting earlier work of Ori [14], of physically relevant black hole spacetimes that admit $C^0$ metric extensions beyond the future Cauchy horizon, while being $C^2$-inextendible, has focused attention on fundamental issues concerning the strong cosmic cen…

In this note we review some aspects of topological censorship. We present several (actually five) alternative sets of hypotheses which allow the proof of a topological censorship theorem for spacetimes with conformal completions at infinity and vanishing cosmological constant.

Theorem proves topological censorship for universes with positive cosmological constant.

Study cosmic structures using Topological Data Analysis and Persistence Energy.

We demonstrate the existence of spherically-symmetric truly naked black holes (TNBH) for which the Kretschmann scalar is finite on the horizon but some curvature components including those responsible for tidal forces as well as the energy density $\barρ$ measured by a free-falling observer are infinite. We choose a ra…

We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983 under the assumption on the surface gravity and generalises previous results due to …

Paper uses ResUNet-CMB to reconstruct cosmic polarization rotation from CMB data.