arXiv research

Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.

Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this …

Unique solutions found for wave-like decaying null infinity equations.

Paper constructs non-symmetric collapsing spacetimes without symmetries.

Extends Minkowski stability proof to minimal decay assumptions.

We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In [5] D. Christodoulou showed that gravitational waves have a nonlinear memory. He discussed how this effect can be measured as a perma…

Proves stability of Minkowski space for specific initial data.

New method proves instability of naked singularity and censors it.

In this paper, we extend the results of Klainerman and Rodnianski in \cite{KR:Trapped}, which were obtained for a finite region, by showing similar results from past null infinity. This allows us to recover and extend the results from past null infinity in the work of Christodoulou \cite{Chr:book}.

Study stability of surfaces in spacetimes, proving new estimates and theorems.

The paper extends Hawking--Page solutions to various spacetimes with singularities.

In a 2004 paper, Lindblad demonstrated that the minimal surface equation on $\mathbb{R}l^{1,1}$ describing graphical time-like minimal surfaces embedded in $\mathbb{R}^{1,2}$ enjoy small data global existence for compactly supported initial data, using Christodoulou's conformal method. Here we give a different, geometr…

New memory effect discovered in gravitational wave behavior.

We extend Eardley and Moncrief's $L^\infty$ estimates for the conformally invariant Yang-Mills-Higgs equations to the Einstein cylinder. Our method is to first work on Minkowski space and localise their estimates, and then carry them to the Einstein cylinder by a conformal transformation. By patching local estimates to…

Extends global stability of Minkowski spacetime to minimal decay assumptions.

New method shows trapped surfaces form in geodesic foliation.

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…

In this paper, we initiate the study of the instability of naked singularities without symmetries. In a series of papers, Christodoulou proved that naked singularities are not stable in the context of the spherically symmetric Einstein equations coupled with a massless scalar field. We study in this paper the next simp…

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

In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in $3+1$ dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations. Con…

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…

Proves local existence and extension principle for Einstein Yang--Mills system with spherical symmetry.

The paper challenges the smooth null infinity model by constructing counter-examples and showing non-smoothness of null infinity.

Klainerman, Luk and Rodnianski derived an anisotropic criterion for formation of trapped surfaces in vacuum, extending the original trapped surface formation theorem of Christodoulou. The effort to understand their result led us to study the intersection of a hyperplane with a lightcone in the Minkowski spacetime. For …

New proof of Minkowski spacetime stability in exterior regions.

Formulae track evolution of angular momentum and center of mass at null infinity.

Survey on stability of Minkowski spacetime in relativity.

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

Study gluing event horizons of Minkowski and Schwarzschild spacetimes.

In a recent seminal paper \cite{D-H-R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solution…

Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.

Study proves global existence and decay for complex wave equations.

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

The paper establishes criteria for spacetime inextendibility using asymptotic volume-distance-ratio analysis.

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

We consider the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, or more generally, in a gauge where the mean curvature of a timelike foliation is fixed near the boundary. We prove the existence of solutions such that the normal to the boundary is tangent to the time slices, the la…

The paper establishes curvature inequalities and rigidity results for surfaces in Riemannian and Lorentzian geometry.

The paper establishes curvature inequalities and rigidity results for CMC and STCMC surfaces in Riemannian and Lorentzian geometry.

Proof confirms cosmic censorship for charged gravitational collapse.

The study identifies obstructions to global visibility of singularities in spacetimes.