Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

CONTENTS
Preface
Contributing Authors
Part I Exact Solutions
Self–gravitating stationary axi-symmetric perfect fluids: Differential rotation
and some geometric features
F.J. Chinea
1
2
3
4
5
Newtonian configurations
Dirichlet boundary problem vs. free-boundary problem
Interior solutions with differential rotation in general relativity
Vacuum as a “perfect fluid”. The “rigid rotation” and the
“irrotational” gauges
Some geometric features of a rigidly rotating perfect fluid interior
solution
New Directions for the New Millennium
Frederick J. Ernst
1 Introduction
2 The Quest for the Geroch Group and its Generalizations
3 The Perfect Fluid Joining Problem
4 Future Directions
4.1 General
4.2 Radiating Axisymmetric Systems
5 Time for a New World Order?
On maximally symmetric and totally geodesic spaces
Alberto Garcia
1 Introduction
2 Killing Equations and Integrability Conditions
3 Maximally Symmetric Spaces
4 Representation of Maximally Symmetric Spaces
5 Maximally Symmetric Sub–spaces
6 Totally Geodesic Hypersurfaces
xv
xvii
3
3
6
7
10
12
15
15
16
18
19
19
20
20
23
23
24
26
29
31
32
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