scholarly journals Total mass‐momentum of arbitrary initial‐data sets in general relativity

1994 ◽  
Vol 35 (8) ◽  
pp. 4157-4177 ◽  
Author(s):  
Robert Geroch ◽  
Shyan‐Ming Perng
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Total Mass ◽  
Data Sets

Gluing Initial Data Sets for General Relativity

2004 ◽  
Vol 93 (8) ◽  
Author(s):  
Piotr T. Chruściel ◽  
James Isenberg ◽  
Daniel Pollack
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Data Sets

Introduction

2020 ◽  
pp. 1-23
Author(s):  
Sergiu Klainerman ◽  
Jérémie Szeftel
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Nonlinear Stability ◽  
Kerr Solution ◽  
Data Sets ◽  
Axially Symmetric ◽  
Kerr Spacetime ◽  
Closed Orbits ◽  
Mathematical Question ◽  
Einstein Vacuum

This introductory chapter provides a quick review of the basic concepts of general relativity relevant to this work. The main object of Albert Einstein's general relativity is the spacetime. The nonlinear stability of the Kerr family is one of the most pressing issues in mathematical general relativity today. Roughly, the problem is to show that all spacetime developments of initial data sets, sufficiently close to the initial data set of a Kerr spacetime, behave in the large like a (typically another) Kerr solution. This is not only a deep mathematical question but one with serious astrophysical implications. Indeed, if the Kerr family would be unstable under perturbations, black holes would be nothing more than mathematical artifacts. The goal of this book is to prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, namely, solutions of the Einstein vacuum equations for asymptotically flat 1 + 3 dimensional Lorentzian metrics which admit a hypersurface orthogonal spacelike Killing vectorfield Z with closed orbits.

scholarly journals The Conformal Flow of Metrics and the General Penrose Inequality

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Qing Han ◽  
Marcus Khuri
Keyword(s):  
Lower Bound ◽  
Initial Data ◽  
Total Mass ◽  
Einstein Equations ◽  
Data Sets ◽  
Penrose Inequality ◽  
General Initial Data ◽  
Time Symmetry ◽  
Conformal Flow ◽  
Special Case

The conformal flow of metrics has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the conformal flow of metrics, so that it may be applied to the Penrose inequality for general initial data sets of the Einstein equations. The Penrose conjecture without the assumption of time symmetry is then reduced to solving a system of PDE with desirable properties.

scholarly journals Construction of N-Body Initial Data Sets in General Relativity

2011 ◽  
Vol 304 (3) ◽  
pp. 637-647 ◽  
Author(s):  
Piotr T. Chruściel ◽  
Justin Corvino ◽  
James Isenberg
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Data Sets

Conformally flat initial data for general relativity in Ashtekar’s variables

1989 ◽  
Vol 39 (2) ◽  
pp. 670-672 ◽  
Author(s):  
Sanjay M. Wagh ◽  
Ravi V. Saraykar
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Conformally Flat ◽  
Ashtekar's Variables

scholarly journals Initial data sets for the Schwarzschild spacetime

2007 ◽  
Vol 75 (2) ◽  
Author(s):  
Alfonso García-Parrado Gómez-Lobo ◽  
Juan A. Valiente Kroon
Keyword(s):  
Initial Data ◽  
Data Sets ◽  
Schwarzschild Spacetime
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