The Cauchy problem for the Einstein equations

By H. Friedrich, A. Rendall. 2000

183 citations recorded by the source corpus.

Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in this context. The question of producing reduced systems of equations which are hyperbolic is examined in detail and some new results on that subject are presented. Relevant background from the theory of partial differential equations is also explained at some length.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9377d4d9790faa0843e34b9ca72e1c6e5f31f086

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Hans Ringstrom
2. András Vasy
3. P. Hintz
4. Eleni-Alexandra Kontou
5. Ko Sanders

In Mathematical Physics

1. Hans Ringstrom
2. Eleni-Alexandra Kontou
3. Ko Sanders

In Nuclear and High Energy Physics

1. Hans Ringstrom
2. András Vasy
3. P. Hintz

Citations in the corpus

• The Bianchi IX Attractor (2000, methodology): “s are concerned, we will restrict our attention to equations of state with 1 ≤ γ≤ 2. The reason is that there is cause to doubt the well posedness of the initial value problem for 2/3 <γ<1, cf. [9] p. 85 and p. 88. Furthermore, in the Bianchi IX case we use results from [14] concerning recolla”
• Future stability of the Einstein-non-linear scalar field system (2008, methodology): “As we shall explain in more detail below, the essential problem is that of proving stability of the metric (4) on R × T n . In order to obtain a hyperbolic problem, we shall use gauge source functions, cf. [ 18 ].”