Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Part I Introduction to gravity and supergravity -- 1 Differential geometry -- 1.1 World tensors -- 1.2 Affinely connected spacetimes -- 1.3 Metric spaces -- 1.3.1 Riemann-Cartan spacetime Ud -- 1.3.2 Riemann spacetime Vd -- 1.4 Tangent space -- 1.4.1 Weitzenböck spacetime Ad -- 1.5 Killing vectors -- 1.6 Duality operations -- 1.7 Differential forms and integration -- 1.8 Extrinsic geometry -- 2 Noether's theorems -- 2.1 Equations of motion -- 2.2 Noether's theorems -- 2.3 Conserved charges -- 2.4 The special-relativistic energy-momentum tensor -- 2.4.1 Conservation of angular momentum -- 2.4.2 Dilatations -- 2.4.3 Rosenfeld's energy-momentum tensor -- 3 A perturbative introduction to general relativity -- 3.1 Scalar SRFTs of gravity -- 3.1.1 Scalar gravity coupled to matter -- 3.1.2 The action for a relativistic massive point-particle -- 3.1.3 The massive point-particle coupled to scalar gravity -- 3.1.4 The action for a massless point-particle -- 3.1.5 The massless point-particle coupled to scalar gravity -- 3.1.6 Self-coupled scalar gravity -- 3.1.7 The geometrical Einstein-Fokker theory -- 3.2 Gravity as a self-consistent massless spin-2 SRFT -- 3.2.1 Gauge invariance, gauge identities, and charge conservation in the SRFT of a spin-1 particle -- 3.2.2 Gauge invariance, gauge identities, and charge conservation in the SRFT of a spin-2 particle -- 3.2.3 Coupling to matter -- 3.2.4 The consistency problem -- 3.2.5 The Noether method for gravity -- 3.2.6 Properties of the gravitational energy-momentum tensor… -- 3.2.7 Deser's argument -- 3.3 General relativity -- 3.4 The Fierz-Pauli theory in a curved background -- 3.4.1 Linearized gravity -- 3.4.2 Massless spin-2 particles in curved backgrounds -- 3.4.3 Self-consistency -- 3.5 Final Comments.

4 Action principles for gravity -- 4.1 The Einstein-Hilbert action -- 4.1.1 Equations of motion -- 4.1.2 Gauge identity and Noether current -- 4.1.3 Coupling to matter -- 4.2 The Einstein-Hilbert action in different conformal frames -- 4.3 The first-order (Palatini) formalism -- 4.3.1 The purely affine theory -- 4.4 The Cartan-Sciama-Kibble theory -- 4.4.1 The coupling of gravity to fermions -- 4.4.2 The coupling to torsion: the CSK theory -- 4.4.3 Gauge identities and Noether currents -- 4.4.4 The first-order Vielbein formalism -- 4.5 Gravity as a gauge theory -- 4.6 Teleparallelism -- 4.6.1 The linearized limit -- 5 N = 1, 2, d = 4 supergravities -- 5.1 Gauging N = 1, d = 4 superalgebras -- 5.2 N = 1, d = 4 (Poincaré) supergravity -- 5.2.1 Local supersymmetry algebra -- 5.3 N = 1, d = 4 AdS supergravity -- 5.3.1 Local supersymmetry algebra -- 5.4 Extended supersymmetry algebras -- 5.4.1 Central extensions -- 5.5 N = 2, d = 4 (Poincaré) supergravity -- 5.6 N = 2, d = 4 "gauged" (AdS) supergravity -- 5.6.1 The local supersymmetry algebra -- 5.7 Proofs of some identities -- 6 Conserved charges in general relativity -- 6.1 The traditional approach -- 6.1.1 The Landau-Lifshitz pseudotensor -- 6.1.2 The Abbott-Deser approach -- 6.2 The Noether approach -- 6.3 The positive-energy theorem -- Part II Gravitating point-particles -- 7 The Schwarzschild black hole -- 7.1 Schwarzschild's solution -- 7.1.1 General properties -- 7.2 Sources for Schwarzschild's solution -- 7.3 Thermodynamics -- 7.4 The Euclidean path-integral approach -- 7.4.1 The Euclidean Schwarzschild solution -- 7.4.2 The boundary terms -- 7.5 Higher-dimensional Schwarzschild metrics -- 7.5.1 Thermodynamics -- 8 The Reissner-Nordström black hole -- 8.1 Coupling a scalar field to gravity and no-hair theorems -- 8.2 The Einstein-Maxwell system -- 8.2.1 Electric charge.

8.2.2 Massive electrodynamics -- 8.3 The electric Reissner-Nordström solution -- 8.4 The Sources of the electric RN black hole -- 8.5 Thermodynamics of RN black holes -- 8.6 The Euclidean electric RN solution and its action -- 8.7 Electric-magnetic duality -- 8.7.1 Poincar duality -- 8.7.2 Magnetic charge: the Dirac monopole and the Dirac quantization condition -- 8.7.3 The Wu-Yang monopole -- 8.7.4 Dyons and the DSZ charge-quantization condition -- 8.7.5 Duality in massive electrodynamics -- 8.8 Magnetic and dyonic RN black holes -- 8.9 Higher-dimensional RN solutions -- 9 The Taub-NUT solution -- 9.1 The Taub-NUT solution -- 9.2 The Euclidean Taub-NUT solution -- 9.2.1 Self-dual gravitational instantons -- 9.2.2 The BPST instanton -- 9.2.3 Instantons and monopoles -- 9.2.4 The BPST instanton and the KK monopole -- 9.2.5 Bianchi IX gravitational instantons -- 9.3 Charged Taub-NUT solutions and IWP solutions -- 10 Gravitational pp-waves -- 10.1 pp-Waves -- 10.1.1 Hpp-waves -- 10.2 Four-dimensional pp-wave solutions -- 10.2.1 Higher-dimensional pp-waves -- 10.3 Sources: the AS shock wave -- 11 The Kaluza-Klein black hole -- 11.1 Classical and quantum mechanics on… -- 11.2 KK dimensional reduction on a circle S -- 11.2.1 The Scherk-Schwarz formalism -- 11.2.2 Newton's constant and masses -- 11.2.3 KK reduction of sources: the massless particle -- 11.2.4 Electric-magnetic duality and the KK action -- 11.2.5 Reduction of the Einstein-Maxwell action and N = 1, d = 5 SUGRA -- 11.3 KK reduction and oxidation of solutions -- 11.3.1 ERN black holes -- 11.3.2 Dimensional reduction of the AS shock wave: the extreme electric KK black hole -- 11.3.3 Non-extreme Schwarzschild and RN black holes -- 11.3.4 Simple KK solution-generating techniques -- 11.4 Toroidal (Abelian) dimensional reduction -- 11.4.1 The 2-torus and the modular group.

11.4.2 Masses, charges and Newton's constant -- 11.5 Generalized dimensional reduction -- 11.5.1 Example 1: a real scalar -- 11.5.2 Example 2: a complex scalar -- 11.5.3 Example 3: an SL(2,R)/SO(2) σ-model -- 11.5.4 Example 4: Wilson lines and GDR -- 11.6 Orbifold compactification -- 12 Dilaton and dilaton/axion black holes -- 12.1 Dilaton black holes: the a-model -- 12.1.1 The a-model solutions in four dimensions -- 12.2 Dilaton/axion black holes -- 12.2.1 The general SWIP solution -- 12.2.2 Supersymmetric SWIP solutions -- 12.2.3 Duality properties of the SWIP solutions -- 12.2.4 N = 2, d = 4 SUGRA solutions -- 13 Unbroken supersymmetry -- 13.1 Vacuum and residual symmetries -- 13.2 Supersymmetric vacua and residual (unbroken) supersymmetries -- 13.2.1 Covariant Lie derivatives -- 13.2.2 Calculation of supersymmetry algebras -- 13.3 N = 1, 2, d = 4 vacuum supersymmetry algebras -- 13.3.1 The Killing-spinor integrability condition -- 13.3.2 The vacua of N = 1, d = 4 Poincar supergravity -- 13.3.3 The vacua of N = 1, d = 4 AdS4 supergravity -- 13.3.4 The vacua of N = 2, d = 4 Poincar supergravity -- 13.3.5 The vacua of N = 2, d = 4 AdS supergravity -- 13.4 The vacua of d = 5, 6 supergravities with eight supercharges -- 13.4.1 N = (1,0), d 6 supergravity -- 13.4.2 N = 1, d = 5 supergravity -- 13.4.3 Relation to the N = 2, d = 4 vacua -- 13.5 Partially supersymmetric solutions -- 13.5.1 Partially unbroken supersymmetry, supersymmetry bounds, and the superalgebra -- 13.5.2 Examples -- Part III Gravitating extended objects of string theory -- 14 String theory -- 14.1 Strings -- 14.1.1 Superstrings -- 14.1.2 Green-Schwarz Actions -- 14.2 Quantum theories of strings -- 14.2.1 Quantization of free-bosonic-string theories -- 14.2.2 Quantization of free-fermionic-string theories -- 14.2.3 D-Branes and O-planes in superstring theories.

14.2.4 String interactions -- 14.3 Compactification on S1: T duality and D-branes -- 14.3.1 Closed bosonic strings on S1 -- 14.3.2 Open bosonic strings on S1 and D-branes -- 14.3.3 Superstrings on S1 -- 15 The string effective action and T duality -- 15.1 Effective actions and background fields -- 15.1.1 The D-brane effective action -- 15.2 T duality and background fields: Buscher's rules -- 15.2.1 T duality in the bosonic-string effective action -- 15.2.2 T duality in the bosonic-string worldsheet action -- 15.2.3 T duality in the bosonic Dp-brane effective action -- 15.3 Example: the fundamental string (F1) -- 16 From eleven to four dimensions -- 16.1 Dimensional reduction from d = 11 to d = 10 -- 16.1.1 11-dimensional supergravity -- 16.1.2 Reduction of the bosonic sector -- 16.1.3 Magnetic potentials -- 16.1.4 Reduction of fermions and the supersymmetry rules -- 16.2 Romans' massive N = 2A, d = 10 supergravity -- 16.3 Further reduction of N = 2A, d = 10 SUEGRA to nine dimensions -- 16.3.1 Dimensional reduction of the bosonic RR sector -- 16.3.2 Dimensional reduction of fermions and supersymmetry rules -- 16.4 The effective-field theory of the heterotic string -- 16.5 Toroidal compactification of the heterotic string -- 16.5.1 Reduction of the action of pure N = 1, d = 10 supergravity -- 16.5.2 Reduction of the fermions and supersymmetry rules of N = 1, d = 10 SUGRA -- 16.5.3 The truncation to pure supergravity -- 16.5.4 Reduction with additional U(1) vector fields -- 16.5.5 Trading the KR 2-form for its dual -- 16.6 T duality, compactification, and supersymmetry -- 17 The type-IIB superstring and type-II T duality -- 17.1 N = 2B, d = 10 supergravity in the string frame -- 17.1.1 Magnetic potentials -- 17.1.2 The type-IIB supersymmetry rules -- 17.2 Type-IIB S duality -- 17.3 Dimensional reduction of N = 2B, d = 10 SUEGRA and type-II T duality.

17.3.1 The type-II T-duality Buscher rules.