arXiv research

Study timelike bounce in charged null dust collapse, identifying key surfaces.

Study of convergence of point-object configurations to a charged dust continuum.

Study spin-0 fields on n-dimensional Minkowski spacetimes, computing asymptotic charges.

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

Solves Einstein vacuum equations gluing problem for close Minkowski data.

Extends Penrose's method to null shells with pressure and energy flux.

Paper proves trapped surface formation for EMCSF system without symmetry assumptions.

Polluting fine dusts in South Korea which are mainly consisted of biomass burning and fugitive dust blown from dust belt is significant problem these days. Predicting concentrations of fine dust particles in Seoul is challenging because they are product of complicate chemical reactions among gaseous pollutants and also…

Match van Stockum dust to vacuum metrics with a single parameter.

Som-Raychaudhuri spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is …

We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three dimensional Euclidean space, and has a natural interpretation in terms of the Penrose ineq…

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

New black hole models with both null and spacelike singularities.

3D dust map of the Milky Way improves resolution and accuracy.

A particular, yet relevant, particular case of the Penrose inequality involves null shells propagating in the Minkowski spacetime. Despite previous claims in the literature, the validity of this inequality remains open. In this paper we rewrite this inequality in terms of the geometry of the surface obtained by interse…

In this paper we analyse semi-linear systems of partial differential equations which are motivated by the conformal formulation of the Einstein constraint equations coupled with realistic physical fields on asymptotically Euclidean (AE) manifolds. In particular, electromagnetic fields give rise to this kind of system. …

Study of caustics in Einstein-dust system, showing spacetime singularities and diverging curvature.

In this paper, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordström family of charged black holes with small charge. Solutions to the linearized Einstein-Maxwell equations around a Reissner-Nordström solution arising from regular initial data remain globally bounded…

Solves C^3 null gluing problem for Einstein vacuum equations.

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…

Second part of series studying charged scalar fields on Reissner--Nordström spacetimes.

Proof confirms cosmic censorship for charged gravitational collapse.

Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.

A non-elementary Möbius group generated by two-parabolics is determined up to conjugation by one complex parameter and the parameter space has been extensively studied. In this paper, we use the results of \cite{GW} to obtain an additional structure for the parameter space, which we term the {\sl two-parabolic space}. …

Making use of the Kerr theorem for shear-free null congruences and of Newman's representation for a virtual charge ``moving'' in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a singular ring uniformly contracting to a point and expanding then to infinity. Elect…

We show that there are isometrically nonequivalent Robertson-Walker metrics which have the same set of geodesics. While one of these metrics satisfies the Einstein equations of pure dust without a cosmological constant, all the other describe pure dust with additional energy momentum tensor of cosmological constant typ…

Unified method for constructing non-vacuum initial data sets in general relativity.

The Kastor-Traschen metric is a time-dependent solution of the Einstein-Maxwell equations with positive cosmological constant $Λ$ which can be used to describe an arbitrary number of charged dynamical black holes. In this paper, we consider the null geodesic structure of this solution, in particular, focusing on the pr…

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

Paper solves Einstein vacuum equations gluing problem with applications.

Proposes MM-DUST for efficient generalized lasso solution paths.

We prove boundedness and polynomial decay statements for solutions to the spin $\pm2$ generalized Teukolsky system on a Reissner-Nordström background with small charge. The first equation of the system is the generalization of the standard Teukolsky equation in Schwarzschild for the extreme component of the curvature $…

Proves symmetries of extremal horizons in spacetimes.

We propose a geometric inequality for two-dimensional spacelike surfaces in the Schwarzschild spacetime. This inequality implies the Penrose inequality for collapsing dust shells in general relativity, as proposed by Penrose and Gibbons. We prove that the inequality holds in several important cases.

New geometry theory solves dark matter issues.

Unified framework for photon and massive particle hypersurfaces in stationary spacetimes.

Study on charged parallel spinors and mass-charge inequalities.

Throughout the literature on the charged Riemannian Penrose inequality, it is generally assumed that there is no charged matter present; that is, the electric field is divergence-free. The aim of this article is to clarify when the charged Riemannian Penrose inequality holds in the presence of charged matter, and when …

We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpinski carpet and the Menger sponge. Our construction is a higher dimensional analogue of Connes' combinatorial construction of the Fredholm module on the Cantor set. We also calculate the Dixmier trace of two operators induced by the …

Two approaches detect EV charging patterns at stations.

Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets

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 counterexample when the charges extend to infinity. We also discuss additional ex…

Charge measurements for instantons and gravitational perturbations.

Scalar-tensor gravitation theories, such as the Brans-Dicke family of theories, are commonly partly described by a modified Einstein equation in which the Ricci tensor is replaced by the Bakry-Émery-Ricci tensor of a Lorentzian metric and scalar field. In physics this formulation is sometimes referred to as the "Jordan…

Researchers resolved ambiguities in gravitational radiation charges.

New approach simplifies proof of wave equations on black holes.

We present a proof of the Riemannian Penrose inequality with charge $r\leq m + \sqrt{m^2-q^2}$, where $A=4πr^2$ is the area of the outermost apparent horizon with possibly multiple connected components, $m$ is the total ADM mass, and $q$ the total charge of a strongly asymptotically flat initial data set for the Einste…

We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to …