Journal ArticleDOI
Hyperbolicity of the 3 + 1 system of einstein equations
TLDR
In this paper, a hyperbolic system from the 3+1 system of Einstein equations with zero shift was obtained by combining the evolution equations with the constraints, and the lapse was chosen by a suitable choice of the lapse, which in a natural way is connected to the space metric.Abstract:
By a suitable choice of the lapse, which in a natural way is connected to the space metric, we obtain a hyperbolic system from the 3+1 system of Einstein equations with zero shift; this is accomplished by combining the evolution equations with the constraints.read more
Citations
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Palatini Approach to Modified Gravity: f(R) Theories and Beyond
TL;DR: A review of the recent literature on modified theories of gravity in the Palatini approach can be found in this paper, where the authors provide an in-depth analysis of the cosmic speedup problem, laboratory and solar systems tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies.
Journal ArticleDOI
Palatini Approach to Modified Gravity: f(R) Theories and Beyond
TL;DR: A review of the recent literature on modified theories of gravity in the Palatini approach is given in this paper, where the authors provide an in-depth analysis of the cosmic speedup problem, laboratory and solar systems tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies.
Book ChapterDOI
The Cauchy problem for the Einstein equations
Helmut Friedrich,Alan D. Rendall +1 more
TL;DR: In this paper, various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations, and a clear explanation of conceptual issues which arise in this context.
Journal ArticleDOI
Numerical relativity and compact binaries
TL;DR: Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the promising sources of gravitational radiation for future detection by gravitational wave observatories as mentioned in this paper.
Journal ArticleDOI
Extrinsic curvature and the Einstein constraints
Harald P. Pfeiffer,James W. York +1 more
TL;DR: In this article, a decomposition of symmetric tensors is used to obtain a weight function such that the transverse traceless part of the extrinsic curvature vanishes.
References
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Journal ArticleDOI
Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires
Journal ArticleDOI
Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
Thomas J. R. Hughes,Thomas J. R. Hughes,Tosio Kato,Tosio Kato,Jerrold E. Marsden,Jerrold E. Marsden +5 more
TL;DR: In this paper, the existence, uniqueness and well-posedness for a general class of quasi-linear hyperbolic evolution equations on a short time interval are established, which are applied to second-order systems on IR, whose solutions lie in the Sobolev space.
Journal ArticleDOI
Propagateurs et commutateurs en relativité générale
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.