Ebook: The Conformal Structure of Space-Time: Geometry, Analysis, Numerics

Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.

---

Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.

---

Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.
Content:
Front Matter....Pages I-XIV
Conformal Einstein Evolution....Pages 1-50
Some Global Results for Asymptotically Simple Space-Times....Pages 51-60
Black Holes....Pages 61-102
Conformal Geometry, Differential Equations and Associated Transformations....Pages 103-112
Twistor Geometry of Conformal Infinity....Pages 113-121
Isotropic Cosmological Singularities....Pages 123-134
Polyhomogeneous Expansions Close to Null and Spatial Infinity....Pages 135-159
Asymptotically Flat and Regular Cauchy Data....Pages 161-181
Construction of Hyperboloidal Initial Data....Pages 183-194
Exploring the Conformal Constraint Equations....Pages 195-222
Criteria for (In)finite Extent of Static Perfect Fluids....Pages 223-237
Problems and Successes in the Numerical Approach to the Conformal Field Equations....Pages 239-259
Some Aspects of the Numerical Treatment of the Conformal Field Equations....Pages 261-282
Data for the Numerical Calculation of the Kruskal Space-Time....Pages 283-295
Numerics of the Characteristic Formulation in Bondi Variables. Where We Are and What Lies Ahead....Pages 297-312
Numerical Experiments at Null Infinity....Pages 313-326
Local Characteristic Algorithms for Relativistic Hydrodynamics....Pages 327-348
Simulations of Generic Singularities in Harmonic Coordinates....Pages 349-358
Some Mathematical and Numerical Questions Connected with First and Second Order Time-Dependent Systems of Partial Differential Equations....Pages 359-370
Back Matter....Pages 371-373

---

Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.
Content:
Front Matter....Pages I-XIV
Conformal Einstein Evolution....Pages 1-50
Some Global Results for Asymptotically Simple Space-Times....Pages 51-60
Black Holes....Pages 61-102
Conformal Geometry, Differential Equations and Associated Transformations....Pages 103-112
Twistor Geometry of Conformal Infinity....Pages 113-121
Isotropic Cosmological Singularities....Pages 123-134
Polyhomogeneous Expansions Close to Null and Spatial Infinity....Pages 135-159
Asymptotically Flat and Regular Cauchy Data....Pages 161-181
Construction of Hyperboloidal Initial Data....Pages 183-194
Exploring the Conformal Constraint Equations....Pages 195-222
Criteria for (In)finite Extent of Static Perfect Fluids....Pages 223-237
Problems and Successes in the Numerical Approach to the Conformal Field Equations....Pages 239-259
Some Aspects of the Numerical Treatment of the Conformal Field Equations....Pages 261-282
Data for the Numerical Calculation of the Kruskal Space-Time....Pages 283-295
Numerics of the Characteristic Formulation in Bondi Variables. Where We Are and What Lies Ahead....Pages 297-312
Numerical Experiments at Null Infinity....Pages 313-326
Local Characteristic Algorithms for Relativistic Hydrodynamics....Pages 327-348
Simulations of Generic Singularities in Harmonic Coordinates....Pages 349-358
Some Mathematical and Numerical Questions Connected with First and Second Order Time-Dependent Systems of Partial Differential Equations....Pages 359-370
Back Matter....Pages 371-373
....