The nonlinear stability of the Minkowski metric in general relativity

1989 ◽  
pp. 128-145 ◽  
Author(s):  
D. Christodoulou ◽  
S. Klainerman
Keyword(s):  
General Relativity ◽  
Nonlinear Stability ◽  
Minkowski Metric

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 790-798
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
General Relativity ◽  
Uncertainty Principle ◽  
Geodesic Equation ◽  
Space Time ◽  
Minimum Length ◽  
Exclusion Zone ◽  
Minkowski Metric ◽  
Time Line ◽  
Geometric Uncertainty ◽  
Classical Gravity

The classical uncertainty principle inequalities are imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle is reformulated in terms of proper space–time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirms the need for a minimum length of space–time line element in the geodesic, which depends on a Lorentz-covariant geodesic-derived scalar. In agreement with quantum gravity theories, GeUP imposes a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone is found around the singularity where uncertainty in space-time diverged to infinity.

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 Classical Treatement of the Compton Collision in General Relativity

1990 ◽  
Vol 142 ◽  
pp. 95-96
Author(s):  
Pierre Paillere
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Transport Theory ◽  
Fundamental Concept ◽  
Minkowski Metric ◽  
Systematic Development

A systematic development of the photon 4-momentum in the non-quantic perspective of General Relativity is very difficult to find in the scientific litterature. However, the photon 4-momentum is a fundamental concept if one wants to study relativistic transport theory or Compton collision formulae. For these reasons, a coherent formalism has been elaborated. It sysmetically allows one to formulate these problems the criterion of validity being the fact that in the case of the Minkowski metric, the general formulae give the classical results of the Special Relativity.

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
General Relativity ◽  
Uncertainty Principle ◽  
Geodesic Equation ◽  
Space Time ◽  
Minimum Length ◽  
Exclusion Zone ◽  
Minkowski Metric ◽  
Time Line ◽  
Geometric Uncertainty ◽  
Classical Gravity

The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.

General Relativity

2006 ◽  
Author(s):  
M. P. Hobson ◽  
G. P. Efstathiou ◽  
A. N. Lasenby
Keyword(s):  
General Relativity
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