Lectures on General Relativity, Cosmology and Quantum Black Holes

PRELIMS.pdf
	Preface
PRELIMS.pdf
	Acknowledgments
PRELIMS.pdf
	Author biography
		Badis Ydri
CH001.pdf
	Chapter 1 General relativity essentials
		1.1 The equivalence principle
CH001.pdf
	Chapter 1 General relativity essentials
		1.2 Relativistic mechanics
CH001.pdf
	Chapter 1 General relativity essentials
		1.3 Differential geometry primer
			1.3.1 Metric manifolds and vectors
CH001.pdf
	Chapter 1 General relativity essentials
		1.3 Differential geometry primer
			1.3.2 Geodesics
CH001.pdf
	Chapter 1 General relativity essentials
		1.3 Differential geometry primer
			1.3.3 Tensors
CH001.pdf
	Chapter 1 General relativity essentials
		1.4 Curvature tensor
			1.4.1 Covariant derivative
CH001.pdf
	Chapter 1 General relativity essentials
		1.4 Curvature tensor
			1.4.2 Parallel transport
CH001.pdf
	Chapter 1 General relativity essentials
		1.4 Curvature tensor
			1.4.3 The Riemann curvature tensor
CH001.pdf
	Chapter 1 General relativity essentials
		1.5 The stress-energy-momentum tensor
			1.5.1 The stress-energy-momentum tensor
CH001.pdf
	Chapter 1 General relativity essentials
		1.5 The stress-energy-momentum tensor
			1.5.2 Perfect fluid
CH001.pdf
	Chapter 1 General relativity essentials
		1.5 The stress-energy-momentum tensor
			1.5.3 Conservation law
			1.5.4 Minimal coupling
CH001.pdf
	Chapter 1 General relativity essentials
		1.6 Einstein’s equation
			1.6.1 Tidal gravitational forces
CH001.pdf
	Chapter 1 General relativity essentials
		1.6 Einstein’s equation
			1.6.2 Geodesic deviation equation
CH001.pdf
	Chapter 1 General relativity essentials
		1.6 Einstein’s equation
			1.6.3 Einsetin’s equation
CH001.pdf
	Chapter 1 General relativity essentials
		1.6 Einstein’s equation
			1.6.4 Newtonian limit
CH001.pdf
	Chapter 1 General relativity essentials
		1.7 Killing vectors and maximally symmetric spaces
CH001.pdf
	Chapter 1 General relativity essentials
		1.8 The Hilbert–Einstein action
CH001.pdf
	Chapter 1 General relativity essentials
		1.9 Exercises
		Exercise 1:
CH001.pdf
	Chapter 1 General relativity essentials
		Solution 1:
		Exercise 2:
		Solution 2:
		Exercise 3:
CH001.pdf
	Chapter 1 General relativity essentials
		Solution 3:
CH001.pdf
	Chapter 1 General relativity essentials
		Exercise 4:
		Solution 4:
CH001.pdf
	Chapter 1 General relativity essentials
		Exercise 5:
		References
CH002.pdf
	Chapter 2 Black holes
		2.1 Spherical star
			2.1.1 The Schwarzschild metric
CH002.pdf
	Chapter 2 Black holes
		2.1 Spherical star
			2.1.2 Particle motion in Schwarzschild spacetime
CH002.pdf
	Chapter 2 Black holes
		2.1 Spherical star
			2.1.3 Precession of perihelia and gravitational redshift
CH002.pdf
	Chapter 2 Black holes
		2.1 Spherical star
			2.1.4 Free fall
CH002.pdf
	Chapter 2 Black holes
		2.2 Schwarzschild black hole
CH002.pdf
	Chapter 2 Black holes
		2.3 The Kruskal–Szekres diagram: maximally extended Schwarzschild solution
CH002.pdf
	Chapter 2 Black holes
		2.4 Various theorems and results
CH002.pdf
	Chapter 2 Black holes
		2.5 Reissner–Nordström (charged) black hole
			2.5.1 Maxwell\'s equations and charges in general relativity
CH002.pdf
	Chapter 2 Black holes
		2.5 Reissner–Nordström (charged) black hole
			2.5.2 Reissner–Nordström solution
CH002.pdf
	Chapter 2 Black holes
		2.5 Reissner–Nordström (charged) black hole
			2.5.3 Extremal Reissner–Nordström black hole
CH002.pdf
	Chapter 2 Black holes
		2.6 Kerr spacetime
			2.6.1 Kerr (rotating) and Kerr–Newman (rotating and charged) black holes
CH002.pdf
	Chapter 2 Black holes
		2.6 Kerr spacetime
			2.6.2 Killing horizons
CH002.pdf
	Chapter 2 Black holes
		2.6 Kerr spacetime
			2.6.3 Surface gravity
CH002.pdf
	Chapter 2 Black holes
		2.6 Kerr spacetime
			2.6.4 Event horizons, ergosphere, and singularity
CH002.pdf
	Chapter 2 Black holes
		2.6 Kerr spacetime
			2.6.5 Penrose process
CH002.pdf
	Chapter 2 Black holes
		2.7 Black hole thermodynamics
CH002.pdf
	Chapter 2 Black holes
		2.8 Exercises
CH002.pdf
	Chapter 2 Black holes
		References
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.1 Homogeneity and isotropy
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.2 Expansion and distances
			3.2.1 Hubble law
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.2 Expansion and distances
			3.2.2 Cosmic distances from standard candles
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.3 Matter, radiation, and vacuum
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.4 Flat Universe
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.5 Closed and open Universes
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.6 Aspects of the early Universe
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.7 The concordance model
		3.8 The Friedmann–Lemaı̂tre–Robertson–Walker (FLRW) metric
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.9 Friedmann equations
			3.9.1 The first Friedmann equation
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.9 Friedmann equations
			3.9.2 Cosmological parameters
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.9 Friedmann equations
			3.9.3 Energy conservation
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.10 Examples of scale factors
			3.10.1 Matter- and radiation-dominated Universes
			3.10.2 Vacuum-dominated Universes
			3.10.3 Milne Universe
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.10 Examples of scale factors
			3.10.4 The static Universe
			3.10.5 Expansion versus recollapse
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.11 Redshift, distances, and age
			3.11.1 Redshift in a flat Universe
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.11 Redshift, distances, and age
			3.11.2 Cosmological redshift
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.11 Redshift, distances, and age
			3.11.3 Comoving and instantaneous physical distances
			3.11.4 Luminosity distance
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.11 Redshift, distances, and age
			3.11.5 Other distances
			3.11.6 Age of the Universe
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		3.12 Exercises
CH003.pdf
	Chapter 3 Cosmology I: The expanding universe
		References
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.1 Cosmological puzzles
			4.1.1 Homogeneity/horizon problem
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.1 Cosmological puzzles
			4.1.2 Flatness problem
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.2 Elements of inflation
			4.2.1 Solving the flatness and horizon problems
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.2 Elements of inflation
			4.2.2 Inflaton
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.2 Elements of inflation
			4.2.3 Amount of inflation
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.2 Elements of inflation
			4.2.4 End of inflation: reheating and scalar-matter-dominated epoch
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.3 Perfect fluid revisited
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.4 Cosmological perturbations
			4.4.1 Metric perturbations
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.4 Cosmological perturbations
			4.4.2 Gauge transformations
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.4 Cosmological perturbations
			4.4.3 Linearized Einstein equations
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.4 Cosmological perturbations
			4.4.4 Explicit calculation of δGˆνμ
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.4 Cosmological perturbations
			4.4.5 Matter perturbations
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.5 Matter–radiation equality
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.6 Hydrodynamical adiabatic scalar perturbations
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.7 Quantum cosmological scalar perturbations
			4.7.1 Slow-roll revisited
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.7 Quantum cosmological scalar perturbations
			4.7.2 Mukhanov action
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.7 Quantum cosmological scalar perturbations
			4.7.3 Quantization and inflationary spectrum
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.8 Rederivation of the Mukhanov action
			4.8.1 Mukhanov action from ADM
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.8 Rederivation of the Mukhanov action
			4.8.2 Power spectra and tensor perturbations
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.8 Rederivation of the Mukhanov action
			4.8.3 CMB temperature anisotropies
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		4.9 Exercises
		Exercises 1:
		Solution 1:
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		Exercise 2:
		Solution 2:
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		Solution 4:
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		Solution 5:
CH004.pdf
	Chapter 4 Cosmology II: the inflationary Universe
		References
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.1 Dark energy
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.2 The cosmological constant
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.3 Elements of quantum field theory in curved spacetime
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.4 Calculation of vacuum energy in curved backgrounds
			5.4.1 Quantization in FLRW Universes
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.4 Calculation of vacuum energy in curved backgrounds
			5.4.2 Instantaneous vacuum
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.4 Calculation of vacuum energy in curved backgrounds
			5.4.3 Quantization in de Sitter spacetime and Bunch–Davies vacuum
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.4 Calculation of vacuum energy in curved backgrounds
			5.4.4 Quantum field theory on curved background with a cutoff
			5.4.5 The conformal limit ξ→1/6
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.5 Is vacuum energy real?
			5.5.1  The Casimir force
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.5 Is vacuum energy real?
			5.5.2. The Dirichlet propagator
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.5 Is vacuum energy real?
			5.5.3. Another derivation using the energy–momentum tensor
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.5 Is vacuum energy real?
			5.5.4 From renormalizable field theory
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.5 Is vacuum energy real?
			5.5.5 Is vacuum energy really real?
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.6 The ADM formulation
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.7 A brief introduction of Hořava–Lifshitz quantum gravity
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.7 A brief introduction of Hořava–Lifshitz quantum gravity
			5.7.1 Lifshitz scalar field theory
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.7 A brief introduction of Hořava–Lifshitz quantum gravity
			5.7.2 Foliation preserving diffeomorphisms and kinetic action
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.7 A brief introduction of Hořava–Lifshitz quantum gravity
			5.7.3. Potential action and detailed balance
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		5.8. Exercises
		Exercise 1:
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		Exercise 2:
		Exercise 3:
		Exercise 4:
		Exercise 5:
CH005.pdf
	Chapter 5 Quantum field theory on curved backgrounds, vacuum energy, and quantum gravity
		Exercise 6:
		Exercise 7:
		Exercise 8:
		Exercise 9:
		Exercise 10:
		References
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.1 Introduction and summary
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.2 Rindler spacetime and general relativity
			6.2.1 Rindler spacetime
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.2 Rindler spacetime and general relativity
			6.2.2 Review of general relativity
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.3 Schwarzschild black holes
			6.3.1 Schwarzschild black holes
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.3 Schwarzschild black holes
			6.3.2 Near horizon coordinates
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.4 Kruskal–Szekres diagram
			6.4.1 Kruskal–Szekres extension and Einstein–Rosen bridge
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.4 Kruskal–Szekres diagram
			6.4.2 Euclidean black hole and thermal field theory
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.5 Density matrix and entanglement
			6.5.1 Density matrix: pure and mixed states
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.5 Density matrix and entanglement
			6.5.2 Entanglement, decoherence, and von Neumann entropy
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.6 Rindler decomposition and Unruh effect
			6.6.1 Rindler decomposition
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.6 Rindler decomposition and Unruh effect
			6.6.2 Unruh temperature
		6.7 Quantum field theory in curved spacetime
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.8 Hawking radiation
			6.8.1 The Unruh effect revisited
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.8 Hawking radiation
			6.8.2 From quantum scalar field theory in a Rindler background
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.8 Hawking radiation
			6.8.3 Summary
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.9 Hawking radiation from quantum field theory in a Schwarzschild background
			6.9.1 Kruskal and Schwarzschild (Boulware) observers and field expansions
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.9 Hawking radiation from quantum field theory in a Schwarzschild background
			6.9.2 Bogolubov coefficients
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.9 Hawking radiation from quantum field theory in a Schwarzschild background
			6.9.3 Hawking radiation and Hawking temperature
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.10 The Unruh versus Boulware vacua: pure to mixed
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.10 The Unruh versus Boulware vacua: pure to mixed
			6.10.1 The adiabatic principle and trans-Planckian reservoir
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.10 The Unruh versus Boulware vacua: pure to mixed
			6.10.2 The Unruh method revisited and Grey body factor
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.10 The Unruh versus Boulware vacua: pure to mixed
			6.10.3 Unruh vacuum state ∣U〉
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.11 The information problem in black hole Hawking radiation
			6.11.1 Information loss, remnants, and unitarity
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.11 The information problem in black hole Hawking radiation
			6.11.2 Information conservation principle
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.11 The information problem in black hole Hawking radiation
			6.11.3 Page curve and Page theorem
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.12 Black hole thermodynamics
			6.12.1 Penrose diagrams
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.12 Black hole thermodynamics
			6.12.2 Bekenstein–Hawking entropy formula
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.12 Black hole thermodynamics
			6.12.3 Brick wall and stretched horizon
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.12 Black hole thermodynamics
			6.12.4 Conclusion
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		6.13 Exercises
		Exercise 1:
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		Exercise 2:
		Exercise 3:
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		Exercise 4:
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		Solution 4:
CH006.pdf
	Chapter 6 Hawking radiation, the information paradox, and black hole thermodynamics
		References
APP.pdf
	Chapter
		A.1 Manifolds
			A.1.1 Maps, open sets and charts
APP.pdf
	Chapter
		A.1 Manifolds
			A.1.2 Manifold: definition and examples
APP.pdf
	Chapter
		A.1 Manifolds
			A.1.3 Vectors and directional derivative
APP.pdf
	Chapter
		A.1 Manifolds
			A.1.4 Dual vectors and tensors
APP.pdf
	Chapter
		A.1 Manifolds
			A.1.5 Metric tensor
APP.pdf
	Chapter
		A.2 Curvature
			A.2.1 Covariant derivative
APP.pdf
	Chapter
		A.2 Curvature
			A.2.2 Parallel transport
APP.pdf
	Chapter
		A.2 Curvature
			A.2.3 The Riemann curvature
APP.pdf
	Chapter
		A.2 Curvature
			A.2.4 Geodesics