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In this paper, under spherical symmetry we prove a trapped surface formation criterion for the Einstein-Maxwell-charged scalar field system. We generalize an approach introduced by Christodoulou for studying the Einstein-scalar field. In…

Analysis of PDEs · Mathematics 2020-05-11 Xinliang An , Zhan Feng Lim

In this paper, we prove a scale-critical trapped surface formation result for the Einstein--Maxwell--charged scalar field (EMCSF) system, without any symmetry assumptions. Specifically, we establish a scale-critical semi-global existence…

Analysis of PDEs · Mathematics 2025-04-29 Dawei Shen , Jingbo Wan

We revisit the classical results of the formation of trapped surfaces for the Einstein vacuum equation relying on the geodesic foliation, rather than the double null foliation used in all previous results, starting with the seminal work of…

General Relativity and Quantum Cosmology · Physics 2024-09-24 Xuantao Chen , Sergiu Klainerman

We consider the formation of trapped surfaces in the evolution of the Einstein-scalar field system without symmetries. To this end, we follow An's strategy to analyse the formation of trapped surfaces in vacuum and for the Einstein-Maxwell…

General Relativity and Quantum Cosmology · Physics 2023-04-05 Peng Zhao , David Hilditch , Juan A. Valiente Kroon

We prove a scale-invariant, semi-global existence result and a trapped surface formation result in the context of coupled Einstein-Yang-Mills theory, without symmetry assumptions. More precisely, we prove a scale-invariant semi-global…

Analysis of PDEs · Mathematics 2023-02-15 Nikolaos Athanasiou , Puskar Mondal , Shing-Tung Yau

In this study we show that, from arbitrarily dispersed initial data, both the concentration of electromagnetic fields and the focusing of gravitational waves could lead to the formation of trapped surfaces. We establish a scale-critical…

Analysis of PDEs · Mathematics 2020-05-27 Xinliang An , Nikolaos Athanasiou

We prove a large-data semi-global existence theorem and the dynamical formation of trapped surfaces for the Einstein-massless Vlasov system in 3+1 dimensions, without any symmetry assumptions. The analysis critically hinges on a finely…

Analysis of PDEs · Mathematics 2025-10-15 Nikolaos Athanasiou , Puskar Mondal , Shing-Tung Yau

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the…

General Relativity and Quantum Cosmology · Physics 2011-03-22 Hakan Andreasson , Gerhard Rein

We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equations of general relativity. We formulate the initial value…

General Relativity and Quantum Cosmology · Physics 2021-06-17 Annegret Y. Burtscher , Philippe G. LeFloch

In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial…

General Relativity and Quantum Cosmology · Physics 2009-12-31 S. Klainerman , I. Rodnianski

We construct infinitely many Einstein-Weyl structures on $S^2 \times R$ of signature (-++) which is sufficiently close to the model case of constant curvature, and whose space-like geodesics are all closed. Such structures are obtained from…

Differential Geometry · Mathematics 2009-11-13 Fuminori Nakata

This is a follow up on our previous work in which we have presented a modified, simpler version of the remarkable recent result of Christodoulou on the formation of trapped surfaces. In this paper we prove two related results. First we…

General Relativity and Quantum Cosmology · Physics 2010-02-16 S. Klainerman , I. Rodnianski

The main results are the following. We derived the matching conditions for the spherically symmetric singular hypersurface (in our case it is equivalent to the world line) in the Weyl$+$Einstein gravity. It was found, that the residual…

General Relativity and Quantum Cosmology · Physics 2019-12-02 Victor Berezin , Vyacheslav Dokuchaev , Yury Eroshenko

In this paper, we study the "minimal requirement" on the incoming radiation that guarantees a trapped surface to form in vacuum. First, we extend the region of existence in Christodoulou's theorem on the formation of trapped surfaces and…

General Relativity and Quantum Cosmology · Physics 2017-04-26 Xinliang An , Jonathan Luk

Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an…

General Relativity and Quantum Cosmology · Physics 2020-05-08 João L. Costa

This paper investigates the global properties of a class of spherically symmetric spacetimes. The class contains the maximal development of asymptotically flat spherically symmetric initial data for a wide variety of coupled Einstein-matter…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Mihalis Dafermos

We present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum. More precisely we provide conditions on null data, concentrated in a neighborhood of a short null geodesic segment (possibly flat everywhere else)…

General Relativity and Quantum Cosmology · Physics 2017-08-02 Sergiu Klainerman , Jonathan Luk , Igor Rodnianski

The purpose of the paper is to understand a mechanism of evolutionary formation of trapped surfaces when there is an electromagnetic field coupled to the background space-time. Based on the short pulse ansatz, on a given finite outgoing…

Analysis of PDEs · Mathematics 2011-05-31 Pin Yu

Further to our consideration on trapped surfaces in gravitational collapse, where pressures were allowed to be negative while satisfying weak energy condition to avoid trapped surface formation, we discuss here several other attempts of…

General Relativity and Quantum Cosmology · Physics 2015-06-30 Pankaj S. Joshi , Rituparno Goswami

Trapped surfaces are studied as inner boundary for the Einstein vacuum constraint equations. The trapped surface condition can be written as a non linear boundary condition for these equations. Under appropriate assumptions, we prove…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Sergio Dain
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