The Cauchy Problem in General Relativity

10.4171/053 ◽  
2009 ◽  
Author(s):  
Hans Ringström
Keyword(s):  
Cauchy Problem ◽  
General Relativity ◽  
The Cauchy Problem

scholarly journals THE EINSTEIN–BOLTZMANN SYSTEM AND POSITIVITY

2013 ◽  
Vol 10 (01) ◽  
pp. 77-104 ◽  
Author(s):  
HO LEE ◽  
ALAN D. RENDALL
Keyword(s):  
Cauchy Problem ◽  
General Relativity ◽  
Boltzmann Equation ◽  
Cross Section ◽  
Collision Cross Section ◽  
Curved Spacetime ◽  
The Boltzmann Equation ◽  
The Cauchy Problem

The Einstein–Boltzmann (EB) system is studied, with particular attention to the non-negativity of the solution of the Boltzmann equation. A new parametrization of post-collisional momenta in general relativity is introduced and then used to simplify the conditions on the collision cross-section given by Bancel and Choquet-Bruhat. The non-negativity of solutions of the Boltzmann equation on a given curved spacetime has been studied by Bichteler and Tadmon. By examining to what extent the results of these authors apply in the framework of Bancel and Choquet-Bruhat, the non-negativity problem for the EB system is resolved for a certain class of scattering kernels. It is emphasized that it is a challenge to extend the existing theory of the Cauchy problem for the EB system so as to include scattering kernels which are physically well-motivated.

scholarly journals Global aspects of the Cauchy problem in general relativity

1969 ◽  
Vol 14 (4) ◽  
pp. 329-335 ◽  
Author(s):  
Yvonne Choquet-Bruhat ◽  
Robert Geroch
Keyword(s):  
Cauchy Problem ◽  
General Relativity ◽  
The Cauchy Problem

scholarly journals THE CAUCHY PROBLEM FOR f(R)-GRAVITY: AN OVERVIEW

2012 ◽  
Vol 09 (01) ◽  
pp. 1250006 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
S. VIGNOLO
Keyword(s):  
Cauchy Problem ◽  
General Relativity ◽  
Scalar Fields ◽  
Conformal Transformations ◽  
Field Equations ◽  
The Cauchy Problem ◽  
Theories Of Gravity ◽  
Matter Fields

We review the Cauchy problem for f(R) theories of gravity, in metric and metric-affine formulations, pointing out analogies and differences with respect to General Relativity. The role of conformal transformations, effective scalar fields and sources in the field equations is discussed in view of the well-formulation and the well-position of the problem. Finally, criteria of viability of the f(R)-models are considered according to the various matter fields acting as sources.

On local and global aspects of the Cauchy problem in general relativity

1999 ◽  
Vol 16 (8) ◽  
pp. R73-R157 ◽  
Author(s):  
Sergiu Klainerman ◽  
Francesco Nicolò
Keyword(s):  
Cauchy Problem ◽  
General Relativity ◽  
The Cauchy Problem
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