The n-body problem in general relativity

T. Levi-Civita9789048183364, 9048183367

Table of contents :
Title ……Page 1
Table of Contents ……Page 3
Translator’s Note ……Page 4
Preface ……Page 5
1. RIEMANN SPACES. SPACE-TIME ……Page 11
2. CONTINUOUS MEDIA ……Page 14
3. THE GRAVITATIONAL EQUATIONS AND THE GEODESIC PRINCIPLE IN CONTINUOUS MEDIA WITHOUT INTERNAL STRESSES ……Page 27
1. UNKNOWN FUNCTIONS AND EQUATIONS ……Page 32
2. ISOMETRIC COORDINATES. REDUCTION TO THE NORMAL FORM ……Page 38
1. ORDERS OF MAGNITUDE AND MAXIMUM USE OF DIMENSIONLESS QUANTITIES ……Page 48
2. REDUCTION OF THE EQUATIONS AND INTEGRATION BY MEANS OF POTENTIALS ……Page 56
1. THE ENERGY TENSOR. PRESSURE AND ITS INVARIANCE ALONG THE WORLD LINES IN THE CASE OF CELESTIAL BODIES ……Page 71
2. RECONSIDERATION OF THE EQUATIONS OF MOTION ……Page 72
3. OVER-ALL CONSEQUENCES FOR EACH BODY ……Page 75
1. THE LAGRANGE FUNCTION ……Page 77
2. THE IMMEDIATE SURROUNDINGS OF A POINT IN MOTION ……Page 79
3. SUPPLEMENTARY CONSIDERATIONS WITH RESPECT TO ORDINARY MECHANICS ……Page 85
4. FURTHER HYPOTHESES LEADING TO ORDINARY DIFFERENTIAL EQUATIONS ……Page 88
5. THE n-BODY PROBLEM ……Page 92
I. THE LAGRANGE FUNCTION FOR THE ABSOLUTE MOTION OF EACH OF TWO BODIES ……Page 101
2. RELATIVE MOTION ……Page 105
3. THE MOTION OF THE CENTER OF GRAVITY ……Page 126
4. AN EXTENSION OF THE DEVICE OF SECTION 1 EMPHASIZING THE ELIMINATION PRINCIPLE IN THE/I-BODY PROBLEM ……Page 128