This is an introductory course on general relativity (GR). We will introduce the physics of curved spacetime, Einstein field equations and their applications to the solar system, black hole physics, gravitational wave astronomy and cosmology.
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26 vidéos4 devoirs
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26 vidéos•Total 230 minutes
What Solutions Do We Care About?•6 minutes
Observational Tests•13 minutes
The Metric in Spherical Symmetry•8 minutes
Simplifications by Coordinate Transformations•11 minutes
Solving R•10 minutes
What If the Sun Suddenly Disappears?•3 minutes
Parameterization to Test GR•7 minutes
Setup•6 minutes
Simplifying Geodesic Equation 1•11 minutes
Simplifying Geodesic Equation 2 & 3•5 minutes
Normalizing λ•10 minutes
Shape of Orbits•6 minutes
Unbound Orbits•10 minutes
How to Observe?•12 minutes
Black Hole Imaging•6 minutes
Gravitational Lensing•9 minutes
Recap: Geodesics & Orbits of Test Particles•12 minutes
Bound Orbits•11 minutes
Mercury Precession•7 minutes
Time Dialation•13 minutes
Who Gets Old Faster?•8 minutes
Shapiro Delay•12 minutes
Effective 1D Problem•5 minutes
For Newtonian & GR Cases•12 minutes
Summary•12 minutes
Remaining Questions•5 minutes
4 devoirs•Total 25 minutes
Spherical Symmetric Vacuum Solution•10 minutes
Geodesics of Test Particles•5 minutes
Orbits of Test Particles and Light•5 minutes
Time Dilation & Delay Effects•5 minutes
Stars and Gravitational Collapse
Module 2•2 heures à terminer
Détails du module
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11 vidéos2 devoirs
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11 vidéos•Total 91 minutes
What to Study About Stars?•7 minutes
How to Model Gravity & Matter?•11 minutes
Einstein's Equations in Both Sides•8 minutes
Solving the Coupled System•12 minutes
Degeneracy Pressure of Fermions•8 minutes
Calculating the Pressure•10 minutes
White Dwarfs: Low Mass Limit•9 minutes
Is GR Important for White Dwarfs?•6 minutes
High Mass Limit & Neutron Stars•7 minutes
Recap: Pressure vs. Collapse•6 minutes
Limit of Stars•8 minutes
2 devoirs•Total 15 minutes
A Spherical Star in GR•5 minutes
White Dwarfs and Neutron Stars•10 minutes
Black Holes
Module 3•5 heures à terminer
Détails du module
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33 vidéos1 devoir
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33 vidéos•Total 317 minutes
What's the Metric Outside & Inside the Shell?•9 minutes
Redshift at R=2GM•12 minutes
Is a Black Hole "Black"?•10 minutes
Does the Black Hole "Remember"?•10 minutes
Where Does Information Go?•11 minutes
Entropy of Black Holes•9 minutes
Are Fundamental Particles Black Holes?•9 minutes
Approaching the Horizon•5 minutes
Across the Horizon•9 minutes
Tortoise Coordinates•9 minutes
Eddington-Finkelstein Coordinates•10 minutes
Kruskal Coordinates•10 minutes
Light Cones in T-R Coordinate•10 minutes
To the End of the World•11 minutes
Do White Holes Exist in Our Universe?•9 minutes
Mapping Infinity to a Finite Range•7 minutes
Penrose Diagrams of Minkowski Spacetime•11 minutes
Recap: Schwarzschild Black Holes•10 minutes
Recap: Kruskal Coordinates•13 minutes
Recap: Penrose Diagrams•9 minutes
Penrose Diagrams of Eternal Black Holes•7 minutes
Cut & Paste of Penrose Diagrams•12 minutes
The Metric of RN Black Holes•9 minutes
Horizons of RN Black Holes•13 minutes
Extremal RN Black Holes•11 minutes
Recap: Penrose Diagrams & RN Black Holes•14 minutes
The Kerr Metric•11 minutes
Stationary Solution & Singularity•7 minutes
Event Horizon of the Kerr Metric•12 minutes
Frame Dragging Effect•9 minutes
Infinite Redshift Surface•5 minutes
Extracting Energy from Black Holes•7 minutes
Summary•8 minutes
1 devoir•Total 5 minutes
Schwarzschild Black Holes•5 minutes
Gravitational Waves
Module 4•3 heures à terminer
Détails du module
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21 vidéos2 devoirs
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21 vidéos•Total 162 minutes
Why Should There Be Gravitational Waves?•4 minutes
What to Study for Gravitational Waves?•12 minutes
Gauge of Gauge Theory•12 minutes
Coulomb Gauge for E&M•7 minutes
Lorenz Gauge for E&M•8 minutes
Coulomb Gauge for Gravity•6 minutes
Linearization of R•5 minutes
Gauge Invariance•9 minutes
Choosing de Donger Gauge•7 minutes
Degrees of Freedom for Gravitational Waves•5 minutes
Propagation of Gravitational Waves•9 minutes
Geodesic Equation for Free Particles•9 minutes
Are the Metric Changes Observable?•10 minutes
Gravitational Wave Events•10 minutes
Recap: Linearization & Detection•5 minutes
Linearized Einstein Equations with Matter•5 minutes
Solution Using the Retarded Green's Function•6 minutes
For Observers Far Away•9 minutes
Quadrupole Formula of GR Radiation•11 minutes
Gravitational Waves from a Binary System•7 minutes
Summary•7 minutes
2 devoirs•Total 35 minutes
Gauge Condition•30 minutes
Detection of Gravitational Waves•5 minutes
Cosmology
Module 5•4 heures à terminer
Détails du module
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25 vidéos3 devoirs
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25 vidéos•Total 219 minutes
Is Cosmology a Natural Science?•14 minutes
Radiation Dominated Universe•10 minutes
Matter Dominated Universe•8 minutes
Where to Start to Study the Universe?•11 minutes
Recap: History of the Universe•7 minutes
The Cosmological Principle•15 minutes
3D Spaces Satisfying the Principle•6 minutes
Light in the Expanding Universe•8 minutes
Perfect Fluid in the Expanding Universe•11 minutes
Solving Continuity Equation•9 minutes
Newtonian Understanding of the Expansion with Matter•8 minutes
Radiation, Matter & Dark Energy Dominated Universes•6 minutes
The Friedmann Equation•5 minutes
Newtonian Understanding of the Expansion with Pressureless Matter•12 minutes
Recap: The Cosmological Principle & Expansion of the Universe•11 minutes
The Expansion History with ω as Constants•8 minutes
Age of the Universe Dominated by Matter & Radiation•6 minutes
Age of the Universe Considering Dark Energy•9 minutes
Causal Structure of the Universe•7 minutes
The Old Horizon Problem•9 minutes
The New Horizon Problem•7 minutes
How to Solve the Horizon Problem?•11 minutes
Inflation Driven by a Scalar Field•11 minutes
Dynamics of the Slow-roll Inflation•10 minutes
Summary•2 minutes
3 devoirs•Total 15 minutes
General Principles of Cosmology•5 minutes
Matter in the Expanding Universe•5 minutes
Inflationary Cosmology•5 minutes
Selected "Advanced" Topics
Module 6•7 heures à terminer
Détails du module
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47 vidéos
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47 vidéos•Total 422 minutes
Question: Why Is Gravity Attractive?•9 minutes
Constructing Separation Vectors•8 minutes
Speed of Spatial Distances Between Geodesics•9 minutes
Acceleration of Spatial Distances Between Geodesics•10 minutes
Decomposition•9 minutes
Rotation & Expansion Scalar•8 minutes
Strong Energy Condition•11 minutes
Weak & Null Energy Condition•7 minutes
Recap: The Raychaudhuri Equation•4 minutes
Why Do We Like Conserved Quantities?•5 minutes
Noether's Theorem•7 minutes
A Mathematical Trick•8 minutes
Symmetry in Space Geometry•10 minutes
The Killing Equation•9 minutes
The Conserved Quantity Along Geodesic•8 minutes
Example: Kerr BH Background•11 minutes
Penrose Process•9 minutes
Relating to Noether's Theorem•6 minutes
Lie Derivative•9 minutes
Recap: Symmetries and Conserved Quantities•3 minutes
Why Is Action the "First Principle"?•12 minutes
The Action Principle•7 minutes
Constructing GR from the First Principle•16 minutes
Variation Principle of Gravity•12 minutes
Variation Principle of Matter•12 minutes
Imposing the Action Principle•10 minutes
ADM Decomposition•12 minutes
Are the Two Tensors the Same?•12 minutes
Recap: The Gravitational Action•1 minute
How to Study the Cosmic Structures?•9 minutes
What Physics to Study?•9 minutes
QFT in Curved Spacetime•8 minutes
Spectator Field in de Sitter Space•12 minutes
Solution Under Uncertainty Principle•9 minutes
Assumption of the Initial State•9 minutes
How to Understand the "Frozen Nonzero"?•12 minutes
How to Study the Statistics of the Galaxy Distribution?•12 minutes
Recap: Origin of Structure from Cosmic Inflation•6 minutes
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