CONTENTS

List of contributors
Preface

1 Introduction
Gary Gibbons and Paul Shellard

1.1 Popular symposium
1.2 Spacetime singularities
1.3 Black holes
1.4 Hawking radiation
1.5 Quantum gravity
1.6 M theory and beyond
1.7 De Sitter space
1.8 Quantum cosmology
1.9 Cosmology
1.10 Postscript

Part 1 Popular symposium

2 Our complex cosmos and its future
Martin Rees

2.1 Introduction
2.2 The universe observed
2.3 Cosmic microwave background radiation
2.4 The origin of large-scale structure
2.5 The fate of the universe
2.6 The very early universe
2.7 Multiverse?
2.8 The future of cosmology

3 Theories of everything and Hawking's wave function of the universe
James Hartle

3.1 Introduction
3.2 Different things fall with the same acceleration in a gravitational field
3.3 The fundamental laws of physics
3.4 Quantum mechanics
3.5 A theory of everything is not a theory of everything
3.6 Reduction
3.7 The main points again References

4 The problem of spacetime singularities: implications for quantum gravity?
Roger Penrose

4.1 Introduction
4.2 Why quantum gravity?
4.3 The importance of singularities
4.4 Entropy
4.5 Hawking radiation and information loss
4.6 The measurement paradox
4.7 Testing quantum gravity?
Useful references for further reading

5 Warping spacetime
Kip Thome

5.1 Introduction
5.2 A first glimpse of the Golden Age: 1964-74
5.3 LISA: mapping black holes with gravitational waves
5.4 The Golden Age again: colliding black holes
5.5 LIGO/VIRGO/GEO: probing colliding black holes with gravitational waves
5.6 Quantum behavior of human-sized objects
5.7 Probing the big bang with gravitational waves
5.8 Cosmic censorship: betting with Stephen
5.9 Time travel
Useful references for further reading

6 Sixty years in a nutshell
Stephen Hawking

6.1 Introduction
6.2 How it began
6.3 General relativity and cosmology
6.4 Mach's principle and Wheeler-Feynman electrodynamics
6.5 The steady state
6.6 Gravity and the expanding universe
6.7 Collapsing stars
6.8 Hawking radiation
6.9 Inflation
6.10 M theory and the future
6.11 Conclusion

Part 2 Spacetime singularities

7 Cosmological perturbations and singularities
George Ellis

7.1 Introduction
Part A: Cosmological perturbations
7.2 Fluids and scalar fields
7.3 Cosmic background radiation
7.4 Issues
Part B: Cosmological singularities
7.5 Analytic direct approach
7.6 Indirect method
7.7 Issues
7.8 Conclusion References

8 The quantum physics of chronology protection
Matt Visser

8.1 Why is chronology protection even an issue?
8.2 Paradoxes and responses
8.3 Elements of chronology protection
8.4 Semiclassical arguments
8.5 The failure of semiclassical gravity
8.6 Where we stand References

9 Energy dominance and the Hawking-Ellis vacuum conservation theorem
Brandon Carter

9.1 Introduction
9.2 The energy dominance condition
9.3 The vacuum conservation theorem References

10 On the instability of extra space dimensions
Roger Penrose

10.1 The issue of functional freedom
10.2 Functional freedom in higher-dimensional theories
10.3 Classical instability of extra dimensions
10.4 The holographic conjecture
References

Part 3 Black holes

11 Black hole uniqueness and the inner horizon stability problem
Werner Israel

11.1 Introduction
11.2 The trailblazers: Moscow 1964
11.3 Cambridge 1965-71
11.4 Descent into the interior
11.5 Internal evolution problem
11.6 Spherical models
11.7 The generic case
11.8 Conclusions
11.9 Acknowledgements
References

12 Black holes in the real universe and their prospects as probes of relativistic gravity
Martin Rees

12.1 Introduction
12.2 Stellar mass holes
12.3 Supermassive holes
12.4 Scenarios for black hole formation
12.5 The galactic context
12.6 Do the candidate holes obey the Kerr metric?
12.7 Gravitational radiation as a probe
References

13 Primordial black holes
Bernard Carr

13.1 Preface
13.2 Historical overview
13.3 PBHs as a probe of primordial inhomogeneities
13.4 PBHs as a probe of cosmological phase transitions
13.5 PBHs as a probe of a varying gravitational constant
13.6 PBHs as a probe of gravitational collapse
13.7 PBHs as a probe of high energy physics
13.8 Postscript References

14 Black hole pair creation
Simon Ross

14.1 Introduction
14.2 Constructing instantons: the C metric
14.3 Calculation of the action
14.4 Pair creation rate
References

15 Black holes at accelerators
Steve Giddings

15.1 Introduction
15.2 TeV-scale gravity
15.3 Black holes on brane worlds
15.4 Black hole decay and signatures
15.5 The future of high energy physics
References

Part 4 Hawking radiation

16 Black holes and string theory
Malcolm Perry

References

17 M theory and black hole quantum mechanics
Joe Polchinski

17.1 A story
17.2 'Finding Stephen's mistake'
17.3 The strong interaction and black holes
References

18 Playing with black strings
Gary Horowitz

18.1 Introduction
18.2 Existence of new (vacuum) solutions
18.3 Properties of the new solutions
18.4 New charged black strings
18.5 Open questions
18.6 Conclusions
References

19 Twenty years of debate with Stephen
Leonard Susskind

19.1 Crisis and paradigm shift
19.2 Stephen's argument for coherence loss
19.3 Horizon Complementarity
19.4 The Holographic Principle
19.5 The ultraviolet/infrared connection
19.6 Counting black hole microstates
19.7 De Sitter space
19.8 Correlations in finite entropy systems References

Part 5 Quantum gravity

20 Euclidean quantum gravity: the view from 2002
Gary Gibbons

20.1 Introduction
20.2 Some historical recollections
20.3 The path integral
20.4 The AdS/CFT correspondence
20.5 The volume canonical ensemble
20.6 Hyperbolic 4-manifolds
20.7 Action and complexity
20.8 Euclides ab omni naevo vindicatus?
References

21 Zeta functions, anomalies and stable branes
Ian Moss

21.1 Introduction
21.2 zeta-functions
21.3 Heat kernel coefficients
21.4 Anomalies
21.5 Brane worlds
21.6 Outlook References

22 Some reflections on the status of conventional quantun theory when applied to quantum gravity
Chris Isham

22.1 Introduction
22.2 The danger of a priori assumptions
22.3 Alternative conceptions of spacetime
22.4 Presheaves and related notions from topos theory
22.5 Presheaves of propositions, and valuations in quantum theory
22.6 Conclusions
References

23 Quantum geometry and its ramifications
Abhay Ashtekar

23.1 Introduction
23.2 A bird's eye view of loop quantum gravity
23.3 Applications of quantum geometry
23.4 Outlook
References

24 Topology change in quantum gravity
Fay Dowker

24.1 Introduction
24.2 A top down framework for topology change
24.3 Morse metrics and elementary topology changes
24.4 Good and bad topology change
24.5 Progress on the Borde-Sorkin conjecture
24.6 Looking to the future References

Part 6 M theory and beyond

25 The past and future of string theory
Edward Witten

26 String theory
David Gross

26.1 Motivations for quantum gravity
26.2 The achievements of string theory
26.3 The future of string theory

27 A brief description of string theory
Michael Green

27.1 Introduction
27.2 Historical background
27.3 String theory today
27.4 Duality and M theory
27.5 Future perspective

28 The story of M
Paul Townsend

28.1 Introduction
28.2 The supermembrane
28.3 Backgrounds of reduced holonomy
28.4 The sigma model limit
References

29 Gauged supergravity and holographic field theory
Nick Warner

29.1 Gauged supergravity and a thesis project
29.2 The ups and downs of maximal gauged supergravity
29.3 Exploring higher dimensions
29.4 Holographic field theory and AdS/CFT correspondence
29.5 Bulk gravity and brane renormalization: where are the branes?
29.6 Holographic renormalization group flows: an example
29.7 Final comments
References

30 57 Varieties in a NUTshell
Ghris Pope

30.1 Introduction
30.2 Four-dimensional self-dual metrics
30.3 Non-compact self-dual 4-metrics
30.4 Compact self-dual 4-metrics: K3
30.5 Special holonomy in higher dimensions
30.6 Ricci-flat Kahler 6-metrics and the conifold
30.7 Seven-dimensional metrics of G2 holonomy
30.8 Spin(7) holonomy
30.9 Conclusion
References

Part 7 De Sitter space

31 Adventures in de Sitter space
Raphael Bousso

31.1 Introduction
31.2 De Sitter space
31.3 Entropy and temperature of event horizons
31.4 Entropy bounds from horizons
31.5 Absolute entropy bounds in spacetimes with A > 0
31.6 Quantum gravity in de Sitter space
31.7 Instabilities of the Nariai solution

32 De Sitter space in non-critical string theory
Andrew Strominger with Alexander Maloney and Eva Silverstein

32.1 Introduction
32.2 De Sitter compactifications of super-critical string theory
32.3 Metastability of the De Sitter vacuum
References

33 Supergravity, M theory and cosmology
Renata Kallosh

33.1 Introduction
33.2 Extended supergravities with dS vacua
33.3 Hybrid inflation with D-branes
33.4 M theory on a four-fold with G-fluxes
References

Part 8 Quantum cosmology

34 The state of the universe
James Hartle

34.1 Introduction
34.2 Final theories
34.3 Effective theories
34.4 Directions References

35 Quantum cosmology
Don Page
35.1 Motivation for a quantum state of the cosmos
35.2 The Hartle-Hawking proposal for the quantum state
35.3 Zero-loop quantum cosmology and FRW-scalar models
35.4 Real classical solutions for the FRW-scalar model
35.5 Complex classical solutions for the FRW-scalar model
35.6 FRW-scalar models with an exponential potential
35.7 Summary
References

36 Quantum cosmology and eternal inflation
Alexander Vilenkin

36.1 Introduction
36.2 Quantum cosmology
36.3 The tunnelling wave function
36.4 Alternative proposals for the wave function
36.5 Semiclassical probabilities
36.6 Comparing different wave functions
36.7 Do we need quantum cosmology?
36.8 Is quantum cosmology testable?
References

37 Probability in the deterministic theory known as quantum mechanics
Bryce DeWitt

37.1 Quantum measurement
37.2 Reality
37.3 Signalling by permutations
37.4 Equal likelihood
37.5 The case of degeneracy
37.6 Unequal probabilities

38 The interpretation of quantum cosmology and the problem of time
Jonathan Halliwell

38.1 Introduction
38.2 The classical case
38.3 The decoherent histories approach to quantum theory
38.4 The induced inner product
38.5 The class operators
38.6 Decoherence and the decoherence functional
38.7 Summary and discussion
References

39 What local supersymmetry can do for quantum cosmology
Peter D'Eath

39.1 Introduction
39.2 No-boundary state
39.3 The classical Riemannian boundary-value problem
39.4 Self-duality
39.5 Canonical quantum theory of N=l supergravity: 'traditional variables'
39.6 Canonical quantization of N=l supergravity: Ashtekar-Jacobson variables
39.7 Comments
References

Part 9 Cosmology

40 Inflation and cosmological perturbations
Alan Guth

40.1 The origin of inflationary fluctuations
40.2 The 1982 Nuffield workshop
40.3 Observational evidence for inflation
40.4 Eternal inflation
40.5 A new singularity theorem
40.6 The origin of the universe
References

41 The future of cosmology: observational anc computational prospects
Paul Shellard

41.1 Empirical cosmology
41.2 The cosmic microwave sky
41.3 Cosmological perturbations and cosmic concordance?
41.4 Critical observational tests
41.5 Primordial gravitational waves
41.6 Computational prospects
41.7 Afterword References

42 The ekpyrotic universe and its cyclic extension
Neil Turok

42.1 Introduction
42.2 Homage to the Ancients
42.3 The ekpyrotic universe model
42.4 The main problem
42.5 Flatness
42.6 Density perturbations
42.7 Brane collisions
42.8 The inter-brane potential
42.9 The cyclic universe
42.10 Back to the singularity
42.11 Conclusions
References

43 Inflationary theory versus the ekpyrotic/cyclic scenaric
Andrei Linde

43.1 Introduction
43.2 Chaotic inflation
43.3 Hybrid inflation
43.4 Quantum fluctuations and density perturbations
43.5 From the Big Bang to eternal inflation
43.6 Inflation and observations
43.7 Alternatives to inflation?
43.8 Ekpyrosis
43.9 Cyclic universe
43.10 Conclusions
References

44 Brane (new) worlds
Pierre Binetruy

44.1 Why study brane cosmology?
44.2 Life on the brane
44.3 AdS/CFT correspondence
44.4 Moduli fields. Moduli space approximation
44.5 Cosmological constant
44.6 Bulk scalars
44.7 Infinite dimensions
44.8 Open problems
References

45 Publications of Stephen Hawking

Index