Gravitational collapse and topology change in spherically symmetric dynamical systems

Péter Csizmadia, I. Rácz

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

A new numerical framework, based on the use of a simple first-order strongly hyperbolic evolution equations, is introduced and tested in the case of four-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable of following the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems is investigated, with particular attention to the evolution in trapped regions. It is verified that, in advance of the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner-Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein-Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are discussed.

Original languageEnglish
Article number015001
JournalClassical and Quantum Gravity
Volume27
Issue number1
DOIs
Publication statusPublished - 2010

Fingerprint

gravitational collapse
dynamical systems
topology
scalars
curvature
gravitation

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Gravitational collapse and topology change in spherically symmetric dynamical systems. / Csizmadia, Péter; Rácz, I.

In: Classical and Quantum Gravity, Vol. 27, No. 1, 015001, 2010.

Research output: Contribution to journalArticle

@article{fd19ac8bac50418d923de274d107e5e1,
title = "Gravitational collapse and topology change in spherically symmetric dynamical systems",
abstract = "A new numerical framework, based on the use of a simple first-order strongly hyperbolic evolution equations, is introduced and tested in the case of four-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable of following the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems is investigated, with particular attention to the evolution in trapped regions. It is verified that, in advance of the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner-Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein-Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are discussed.",
author = "P{\'e}ter Csizmadia and I. R{\'a}cz",
year = "2010",
doi = "10.1088/0264-9381/27/1/015001",
language = "English",
volume = "27",
journal = "Classical and Quantum Gravity",
issn = "0264-9381",
publisher = "IOP Publishing Ltd.",
number = "1",

}

TY - JOUR

T1 - Gravitational collapse and topology change in spherically symmetric dynamical systems

AU - Csizmadia, Péter

AU - Rácz, I.

PY - 2010

Y1 - 2010

N2 - A new numerical framework, based on the use of a simple first-order strongly hyperbolic evolution equations, is introduced and tested in the case of four-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable of following the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems is investigated, with particular attention to the evolution in trapped regions. It is verified that, in advance of the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner-Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein-Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are discussed.

AB - A new numerical framework, based on the use of a simple first-order strongly hyperbolic evolution equations, is introduced and tested in the case of four-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable of following the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems is investigated, with particular attention to the evolution in trapped regions. It is verified that, in advance of the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner-Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein-Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are discussed.

UR - http://www.scopus.com/inward/record.url?scp=73649128576&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73649128576&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/27/1/015001

DO - 10.1088/0264-9381/27/1/015001

M3 - Article

VL - 27

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 1

M1 - 015001

ER -