CONTENTS -- Preface -- ACKNOWLEDGMENTS -- Part I: From Newton to Einstein Paradigm Shifts -- 1. Development of the Concepts of Space, Time and Space-Time from Newton to Einstein J. Stachel -- 1. Introduction: The Changing Nature of Change -- 2. The Bronstein Cube -- 3. Demokritos versus Aristotle: `Space' versus `Place' -- 4. Absolute versus Relational Concepts of Space and Time -- 5. Universal Temporal Order -- 6. Relative Space -- 7. Relative Time -- 8. Fixed Kinematical Structure -- 9. Fetishism of Mathematics -- 10. Four-Dimensional Formulation -- 11. Enter Gravitation: General Non-Relativity -- 12. Dynamizing the Inertial Structure -- 13. General Relativity -- 14. Di erentiable Manifolds, Fiber Bundlesll -- 15. The General-Relativistic Revolution -- 16. The Second Relativization of Time -- 17. What is the Question? -- Acknowledgement -- References -- Part II: Einstein's Universe Rami cations of General Relativity -- 2. Gravitational Billiards, Dualities and Hidden Symmetries H. Nicolai -- 1. Introduction -- Is Einstein's theory integrable? -- What is the symmetry underlying M Theory? -- 2. Known Duality Symmetries -- 2.1. Linearized duality -- 2.2. A nonlinear duality: the Geroch group -- 3. Gravitational Billiards and Kac-Moody Algebras -- 3.1. BKL dynamics and gravitational billiards -- 3.2. Emergence of Kac Moody symmetries -- 3.3. The main conjecture -- 4. Basics of Kac Moody Theory -- 5. The Hyperbolic Kac Moody Algebra AE3 -- 6. Nonlinear -Models in One Dimension -- 7. Finale: E10 { The Ultimate Symmetry? -- Acknowledgments -- References -- 3. The Nature of Spaceime Singularities A. D. Rendall -- 1. Introduction -- 2. Cosmological Singularities -- 3. Black Hole Singularities -- 4. Shells and Shocks -- 5. Critical Collapse -- 6. Conclusion -- References -- 4. Black Holes - An Introduction P. T. Chrusciel -- 1. Stationary Black Holes.

1.1. Asymptotically flat examples -- 1.2. 0 -- 1.3. Black strings and branes -- 2. Model Independent Concepts -- 3. Classification of Asymptotically Flat Stationary Black Holes ("No hair theorems") -- 4. Dynamical Black Holes: Robinson-Trautman Metrics -- 5. Initial Data Sets Containing Trapped, or Marginally Trapped, Surfaces -- 5.1. Brill-Lindquist initial data -- 5.2. The "many Schwarzschild" initial data -- 5.3. Black holes and gluing methods -- Acknowledgements -- References -- 5. The Physical Basis of Black Hole Astrophysics R. H. Price -- 1. Introduction -- I. Frozen or continuous collapse? -- II. Observing the unobservable black hole -- III. Newtonian-like points, or spacetime regions -- IV. Black holes: simple or exceedingly unsimple -- 2. Stationary Black Hole Spacetimes -- 3. Particles and Fields Near Black Holes -- 3.1. Particle worldlines -- 3.2. Radial orbits -- 3.3. Nonradial orbits -- 3.4. Field dynamics -- 4. Observational Black Holes -- 4.1. General considerations -- 4.2. Black hole mass ranges -- 4.3. Accretion, dynamos and luminosity -- 4.4. Exotic orbits, galactic centers, and gravitational waves -- 5. Dynamical Black Holes -- 6. Conclusion -- I. Frozen or continuous collapse? -- II. Observing the unobservable black hole -- III. Newtonian-like points, or spacetime regions -- IV. Black holes: simple or exceedingly unsimple -- Acknowledgments -- References -- 6. Probing Space-Time Through Numerical Simulations P. Laguna -- 1. Multi-Faceted Numerical Relativity -- 2. Geometrodynamics and Numerical Evolutions -- 3. Black Hole Excision: Space-time Surgery -- 4. Initial Data: The Astrophysical Connection -- 5. Gauge Conditions -- 6. Extracting Observables: Connecting with Data Analysis -- 7. Imagining the Future -- Acknowledgments -- Appendix A. The ADM Formulation -- Appendix B. York's Conformal Approach -- References.

7. Understanding Our Universe: Current Status and Open Issues T. Padmanabhan -- 1. Prologue: Universe as a Physical System -- 2. The Cosmological Paradigm -- 3. Growth of Structures in the Universe -- 4. Inflation and Generation of Initial Perturbations -- 5. Temperature Anisotropies of the CMBR -- 6. The Dark Energy -- 7. For the Snark was a Boojum, You See -- 8. Deeper Issues in Cosmology -- References -- 8. Was Einstein Right? Testing Relativity at the Centenary C. M. Will -- 1. Introduction -- 2. The Einstein Equivalence Principle -- 2.1. Tests of the weak equivalence principle -- 2.2. Tests of local Lorentz invariance -- 2.3. Tests of local position invariance -- 3. Solar-System Tests -- 3.1. The parametrized post-Newtonian framework -- 3.2. Bounds on the PPN parameters -- 3.3. Gravity Probe-B -- 4. The Binary Pulsar -- 5. Gravitational-Wave Tests of Gravitation Theory -- 5.1. Polarization of gravitational waves -- 5.2. Speed of gravitational waves -- 5.3. Tests of scalar-tensor gravity -- 6. Conclusions -- References -- 9. Receiving Gravitational Waves P. R. Saulson -- 1. Introduction -- 2. Origin of the Idea of Gravitational Waves and Gravitational Wave Detectors -- 3. Free-Mass Gravitational Wave Detectors -- 4. A Gedanken Experiment to Detect a Gravitational Wave -- 5. First Steps from Thought Experiment to Real Experiment -- 6. Further Advances -- 7. First Steps Toward Kilometer-Scale Interferometers -- 8. LIGO Moves Forward -- 9. Construction, Installation, and Commissioning -- 10. Are We There Yet? -- Acknowledgments -- References -- 10. Relativity in the Global Positioning System N. Ashby -- 1. Introduction -- 2. Reference Frames and the Sagnac Effect -- 3. GPS Coordinate Time and TAI -- 4. The Realization of Coordinate Time -- 5. Relativistic Effects on Satellite Clocks -- 6. TOPEX/POSEIDON Relativity Experiment -- 7. Doppler Effect.

8. Crosslink Ranging -- 9. Frequency Shifts Induced by Orbit Changes -- 10. Secondary Relativistic Effects -- 11. Applications -- 12. Conclusions -- References -- Part III: Beyond Einstein Unifying General Relativity with Quantum Physics -- 11. Spacetime in Semiclassical Gravity L. H. Ford -- 1. Introduction -- 2. Renormalization of (T) -- 3. The Stability Problem in the Semiclassical Theory -- 4. The Hawking Effect -- 5. Quantum Effects in the Early Universe -- 6. The Dark Energy Problem -- 7. Negative Energy Density for Quantum Fields -- 8. Some Possible Consequences of Quantum Violation of Classical Energy Conditions -- 8.1. Singularity avoidance -- 8.2. Creation of naked singularities -- 8.3. Violation of the second law of thermodynamics? -- 8.4. Traversable wormholes and warp drive spacetimes -- 9. Quantum Inequalities -- 9.1. Violations of the second law and of cosmic censorship -- 9.2. Constraints on traversable wormholes and warp drive -- 10. Beyond Semiclassical Gravity: Fluctuations -- 11. Summary -- Acknowledgments -- References -- 12. Space Time in String Theory T. Banks -- 1. Introduction -- 2. Branes, Charges and BPS States -- 3. 11 - 2 = 10 -- 4. 11 - 4 = 10 -- 5. The AdS/CFT Correspondence -- 5.1. Potentials and domain walls -- 5.2. SUSY and large radius AdS space -- 6. The Real World: SUSY Breaking and dS Space -- 7. A Theory of Stable de Sitter Space -- 8. Towards a Holographic Theory of Space-Time -- 9. Conclusions -- References -- 13. Quantum Geometry and Its Rami cations A. Ashtekar -- 1. Setting the Stage -- 2. A Bird's Eye View of Loop Quantum Gravity -- 2.1. Viewpoint -- 2.2. Quantum Geometry -- 2.3. Quantum dynamics -- 3. Applications of Quantum Geometry -- 3.1. Black-holes -- 3.2. Big bang -- 4. Summary and Outlook -- Acknowledgments -- References -- 14. Loop Quantum Cosmology M. Bojowald -- 1. Introduction.

2. Classical Cosmology -- 3. Quantum Gravity -- 3.1. Indications -- 3.2. Early quantum cosmology -- 3.3. Loop quantum gravity -- 4. Quantum Cosmology -- 4.1. Representation -- 4.2. Quantum evolution -- 4.2.1. Difference equation -- 4.2.2. Meaning of the wave function -- 4.3. Densities -- 4.3.1. Quantization -- 4.3.2. Confirmation of indications -- 4.4. Phenomenology -- 4.4.1. Bounces -- 4.4.2. Inflation -- 5. Conclusions and Outlook -- References -- 15. Consistent Discrete Space-Time R. Gambini and J. Pullin -- 1. Introduction -- 2. Consistent Discretizations -- 3. The Rovelli Model -- 4. Applications in Classical and Quantum Cosmology -- 5. Fundamental Decoherence and Other Quantum Applications -- 6. Connections with Continuum Loop Quantum Gravity -- 7. Discussion and Frequently Asked Questions -- 8. Conclusions -- Acknowledgments -- References -- 16. Causal Sets and the Deep Structure of Spacetime F. Dowker -- 1. Introduction -- 2. Kinematics -- 2.1. The causal set -- 2.2. An analogy: discrete matter -- 2.3. Discrete spacetime -- 2.4. Reassessed in a quantal light -- 3. Dynamics -- 3.1. A histories framework for quantum causal sets -- 3.2. A classical warm up -- 3.3. The problem of general covariance -- 3.4. The problem of Now -- 3.5. The quantum case -- 4. Conclusions -- Acknowledgments -- References -- 17. The Twistor Approach to Space-Time Structures R. Penrose -- 1. Early Motivations and Fundamental Basis of Twistor Theory -- 2. Basic Twistor Geometry and Algebra -- 3. Momentum and Angular Momentum for Massless Particles -- 4. Massless Fields and their Twistor Contour Integrals -- 5. Twistor Sheaf Cohomology -- 6. The Non-Linear Graviton -- 7. The Googly Problem -- Further Developments -- Acknowledgments -- Notes -- References -- Index.