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Table of Contents
Intro; Preface; Contents; Notations; mk1; mk2; Classical Treatment; 1 Geometrical Introduction; 1 Spacetimes; 2 Local Geodesic Structure; 2.1 Geodesics; 2.2 Normal, Convex and Simple Neighbourhoods; 3 The Time; 3.1 The Past and the Future; 3.2 Causality Condition; 3.3 Causally Convex and Strongly Causal Sets; 4 Global Hyperbolicity; 5 Perfectly Simple Spacetimes; 6 `Cutting and Pasting' Spacetimes; 6.1 Gluing Spacetimes Together; 6.2 Ungluing Spacetimes; 2 Physical Predilections; 1 Locality; 1.1 C-Spaces; 1.2 The Weak Energy Condition (WEC); 2 The Maximal Speed and Causality
2.1 The Speed to Be Restricted2.2 Cause-Effect Relation; 2.3 The Principle of Causality; 2.4 `The Speed of Gravity' vspscsps; 2.5 The `Semi-superluminal' Velocity; 3 Evolutionary Picture; 3.1 Is the Universe Globally Hyperbolic?; 3.2 Should General Relativity Be Slightly Modified?; 3.3 Matter in Non-globally Hyperbolic Spacetimes; 3 Shortcuts; 1 The Concept of Shortcut; 2 Wormholes; 2.1 What Are Wormholes?; 2.2 Wormholes as a Means of Transport; 3 Warp Drives; 4 Time Machines; 1 The Time Machine; 2 Misner-Type Time Machines; 2.1 Misner Space; 2.2 (Anti-) de Sitter Time Machines
2.3 Some Global Effects3 Wormholes as Time Machines; 4 Special Types of Cauchy Horizons; 4.1 Imprisoned Geodesics and Compactly Determined Horizons; 4.2 Deformation of Imprisoned Geodesics; 4.3 Some Properties of Time Machines with CG(D)CH; 5 A Pathology-Free Time Machine; 5 A No-Go Theorem for the Artificial Time Machine; 1 The Theorem and Its Interpretation; 2 Outline of the Proof; 3 Convexly c-Extendible Sets; 4 Construction of M""36; 4.1 The Spacetime M; 4.2 The Spacetime M; 4.3 The Spacetime M""36; 5 The Structure of M""36; 5.1 The Surfaces S and S; 5.2 Convex C-Extendibility of M""36
6 Proof of the Theorem6 Time Travel Paradoxes; 1 The Essence of the Problem; 1.1 The Two Kinds of Time Travel Paradoxes; 1.2 Pseudoparadoxes; 2 Science Fiction; 2.1 The Banana Skin Principle; 2.2 Restrictions on the Freedom of the Will; 3 Modelling and Demystification of the Paradoxes; 3.1 The Grandfather Paradox; 3.2 The Machine Builder Paradox ttrpar; Semiclassical Effects; 7 Quantum Corrections; 1 Direct Calculation; 2 Auxiliary Spacetimes; 2.1 Conformal Coupling; 2.2 The Method of Images; 8 WEC-Related Quantum Restrictions; 1 Quantum Restrictions on Shortcuts; 1.1 The Quantum Inequality
1.2 Connection with Shortcuts1.3 The Meaning of the Restrictions; 2 Counterexamples; 2.1 The Weyl Tensor; 2.2 The Non-trivial Topology; 2.3 `Economical' Shortcuts; 9 Primordial Wormhole; 1 Introduction; 2 The Model and Assumptions; 2.1 Schwarzschild Spacetime; 2.2 The Geometry of the Evaporating Wormhole; 2.3 Weak Evaporation Assumption; 2.4 Preliminary Discussion; 3 The Evolution of the Horizon; 3.1 Evaporation; 3.2 The Shift of the Horizon; 4 The Traversability of the Wormhole; 10 At and Beyond the Horizon; A Details; A.1 Externally Flat Wormhole as Charge
2.1 The Speed to Be Restricted2.2 Cause-Effect Relation; 2.3 The Principle of Causality; 2.4 `The Speed of Gravity' vspscsps; 2.5 The `Semi-superluminal' Velocity; 3 Evolutionary Picture; 3.1 Is the Universe Globally Hyperbolic?; 3.2 Should General Relativity Be Slightly Modified?; 3.3 Matter in Non-globally Hyperbolic Spacetimes; 3 Shortcuts; 1 The Concept of Shortcut; 2 Wormholes; 2.1 What Are Wormholes?; 2.2 Wormholes as a Means of Transport; 3 Warp Drives; 4 Time Machines; 1 The Time Machine; 2 Misner-Type Time Machines; 2.1 Misner Space; 2.2 (Anti-) de Sitter Time Machines
2.3 Some Global Effects3 Wormholes as Time Machines; 4 Special Types of Cauchy Horizons; 4.1 Imprisoned Geodesics and Compactly Determined Horizons; 4.2 Deformation of Imprisoned Geodesics; 4.3 Some Properties of Time Machines with CG(D)CH; 5 A Pathology-Free Time Machine; 5 A No-Go Theorem for the Artificial Time Machine; 1 The Theorem and Its Interpretation; 2 Outline of the Proof; 3 Convexly c-Extendible Sets; 4 Construction of M""36; 4.1 The Spacetime M; 4.2 The Spacetime M; 4.3 The Spacetime M""36; 5 The Structure of M""36; 5.1 The Surfaces S and S; 5.2 Convex C-Extendibility of M""36
6 Proof of the Theorem6 Time Travel Paradoxes; 1 The Essence of the Problem; 1.1 The Two Kinds of Time Travel Paradoxes; 1.2 Pseudoparadoxes; 2 Science Fiction; 2.1 The Banana Skin Principle; 2.2 Restrictions on the Freedom of the Will; 3 Modelling and Demystification of the Paradoxes; 3.1 The Grandfather Paradox; 3.2 The Machine Builder Paradox ttrpar; Semiclassical Effects; 7 Quantum Corrections; 1 Direct Calculation; 2 Auxiliary Spacetimes; 2.1 Conformal Coupling; 2.2 The Method of Images; 8 WEC-Related Quantum Restrictions; 1 Quantum Restrictions on Shortcuts; 1.1 The Quantum Inequality
1.2 Connection with Shortcuts1.3 The Meaning of the Restrictions; 2 Counterexamples; 2.1 The Weyl Tensor; 2.2 The Non-trivial Topology; 2.3 `Economical' Shortcuts; 9 Primordial Wormhole; 1 Introduction; 2 The Model and Assumptions; 2.1 Schwarzschild Spacetime; 2.2 The Geometry of the Evaporating Wormhole; 2.3 Weak Evaporation Assumption; 2.4 Preliminary Discussion; 3 The Evolution of the Horizon; 3.1 Evaporation; 3.2 The Shift of the Horizon; 4 The Traversability of the Wormhole; 10 At and Beyond the Horizon; A Details; A.1 Externally Flat Wormhole as Charge