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 Videos4 Aufgaben
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26 Videos•Insgesamt 230 Minuten
What Solutions Do We Care About?•6 Minuten
Observational Tests•13 Minuten
The Metric in Spherical Symmetry•8 Minuten
Simplifications by Coordinate Transformations•11 Minuten
Solving R•10 Minuten
What If the Sun Suddenly Disappears?•3 Minuten
Parameterization to Test GR•7 Minuten
Setup•6 Minuten
Simplifying Geodesic Equation 1•11 Minuten
Simplifying Geodesic Equation 2 & 3•5 Minuten
Normalizing λ•10 Minuten
Shape of Orbits•6 Minuten
Unbound Orbits•10 Minuten
How to Observe?•12 Minuten
Black Hole Imaging•6 Minuten
Gravitational Lensing•9 Minuten
Recap: Geodesics & Orbits of Test Particles•12 Minuten
Bound Orbits•11 Minuten
Mercury Precession•7 Minuten
Time Dialation•13 Minuten
Who Gets Old Faster?•8 Minuten
Shapiro Delay•12 Minuten
Effective 1D Problem•5 Minuten
For Newtonian & GR Cases•12 Minuten
Summary•12 Minuten
Remaining Questions•5 Minuten
4 Aufgaben•Insgesamt 25 Minuten
Spherical Symmetric Vacuum Solution•10 Minuten
Geodesics of Test Particles•5 Minuten
Orbits of Test Particles and Light•5 Minuten
Time Dilation & Delay Effects•5 Minuten
Stars and Gravitational Collapse
Modul 2•2 Stunden abzuschließen
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11 Videos2 Aufgaben
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11 Videos•Insgesamt 91 Minuten
What to Study About Stars?•7 Minuten
How to Model Gravity & Matter?•11 Minuten
Einstein's Equations in Both Sides•8 Minuten
Solving the Coupled System•12 Minuten
Degeneracy Pressure of Fermions•8 Minuten
Calculating the Pressure•10 Minuten
White Dwarfs: Low Mass Limit•9 Minuten
Is GR Important for White Dwarfs?•6 Minuten
High Mass Limit & Neutron Stars•7 Minuten
Recap: Pressure vs. Collapse•6 Minuten
Limit of Stars•8 Minuten
2 Aufgaben•Insgesamt 15 Minuten
A Spherical Star in GR•5 Minuten
White Dwarfs and Neutron Stars•10 Minuten
Black Holes
Modul 3•5 Stunden abzuschließen
Moduldetails
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33 Videos1 Aufgabe
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33 Videos•Insgesamt 317 Minuten
What's the Metric Outside & Inside the Shell?•9 Minuten
Redshift at R=2GM•12 Minuten
Is a Black Hole "Black"?•10 Minuten
Does the Black Hole "Remember"?•10 Minuten
Where Does Information Go?•11 Minuten
Entropy of Black Holes•9 Minuten
Are Fundamental Particles Black Holes?•9 Minuten
Approaching the Horizon•5 Minuten
Across the Horizon•9 Minuten
Tortoise Coordinates•9 Minuten
Eddington-Finkelstein Coordinates•10 Minuten
Kruskal Coordinates•10 Minuten
Light Cones in T-R Coordinate•10 Minuten
To the End of the World•11 Minuten
Do White Holes Exist in Our Universe?•9 Minuten
Mapping Infinity to a Finite Range•7 Minuten
Penrose Diagrams of Minkowski Spacetime•11 Minuten
Recap: Schwarzschild Black Holes•10 Minuten
Recap: Kruskal Coordinates•13 Minuten
Recap: Penrose Diagrams•9 Minuten
Penrose Diagrams of Eternal Black Holes•7 Minuten
Cut & Paste of Penrose Diagrams•12 Minuten
The Metric of RN Black Holes•9 Minuten
Horizons of RN Black Holes•13 Minuten
Extremal RN Black Holes•11 Minuten
Recap: Penrose Diagrams & RN Black Holes•14 Minuten
The Kerr Metric•11 Minuten
Stationary Solution & Singularity•7 Minuten
Event Horizon of the Kerr Metric•12 Minuten
Frame Dragging Effect•9 Minuten
Infinite Redshift Surface•5 Minuten
Extracting Energy from Black Holes•7 Minuten
Summary•8 Minuten
1 Aufgabe•Insgesamt 5 Minuten
Schwarzschild Black Holes•5 Minuten
Gravitational Waves
Modul 4•3 Stunden abzuschließen
Moduldetails
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21 Videos2 Aufgaben
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21 Videos•Insgesamt 162 Minuten
Why Should There Be Gravitational Waves?•4 Minuten
What to Study for Gravitational Waves?•12 Minuten
Gauge of Gauge Theory•12 Minuten
Coulomb Gauge for E&M•7 Minuten
Lorenz Gauge for E&M•8 Minuten
Coulomb Gauge for Gravity•6 Minuten
Linearization of R•5 Minuten
Gauge Invariance•9 Minuten
Choosing de Donger Gauge•7 Minuten
Degrees of Freedom for Gravitational Waves•5 Minuten
Propagation of Gravitational Waves•9 Minuten
Geodesic Equation for Free Particles•9 Minuten
Are the Metric Changes Observable?•10 Minuten
Gravitational Wave Events•10 Minuten
Recap: Linearization & Detection•5 Minuten
Linearized Einstein Equations with Matter•5 Minuten
Solution Using the Retarded Green's Function•6 Minuten
For Observers Far Away•9 Minuten
Quadrupole Formula of GR Radiation•11 Minuten
Gravitational Waves from a Binary System•7 Minuten
Summary•7 Minuten
2 Aufgaben•Insgesamt 35 Minuten
Gauge Condition•30 Minuten
Detection of Gravitational Waves•5 Minuten
Cosmology
Modul 5•4 Stunden abzuschließen
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25 Videos3 Aufgaben
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25 Videos•Insgesamt 219 Minuten
Is Cosmology a Natural Science?•14 Minuten
Radiation Dominated Universe•10 Minuten
Matter Dominated Universe•8 Minuten
Where to Start to Study the Universe?•11 Minuten
Recap: History of the Universe•7 Minuten
The Cosmological Principle•15 Minuten
3D Spaces Satisfying the Principle•6 Minuten
Light in the Expanding Universe•8 Minuten
Perfect Fluid in the Expanding Universe•11 Minuten
Solving Continuity Equation•9 Minuten
Newtonian Understanding of the Expansion with Matter•8 Minuten
Radiation, Matter & Dark Energy Dominated Universes•6 Minuten
The Friedmann Equation•5 Minuten
Newtonian Understanding of the Expansion with Pressureless Matter•12 Minuten
Recap: The Cosmological Principle & Expansion of the Universe•11 Minuten
The Expansion History with ω as Constants•8 Minuten
Age of the Universe Dominated by Matter & Radiation•6 Minuten
Age of the Universe Considering Dark Energy•9 Minuten
Causal Structure of the Universe•7 Minuten
The Old Horizon Problem•9 Minuten
The New Horizon Problem•7 Minuten
How to Solve the Horizon Problem?•11 Minuten
Inflation Driven by a Scalar Field•11 Minuten
Dynamics of the Slow-roll Inflation•10 Minuten
Summary•2 Minuten
3 Aufgaben•Insgesamt 15 Minuten
General Principles of Cosmology•5 Minuten
Matter in the Expanding Universe•5 Minuten
Inflationary Cosmology•5 Minuten
Selected "Advanced" Topics
Modul 6•7 Stunden abzuschließen
Moduldetails
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47 Videos
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47 Videos•Insgesamt 422 Minuten
Question: Why Is Gravity Attractive?•9 Minuten
Constructing Separation Vectors•8 Minuten
Speed of Spatial Distances Between Geodesics•9 Minuten
Acceleration of Spatial Distances Between Geodesics•10 Minuten
Decomposition•9 Minuten
Rotation & Expansion Scalar•8 Minuten
Strong Energy Condition•11 Minuten
Weak & Null Energy Condition•7 Minuten
Recap: The Raychaudhuri Equation•4 Minuten
Why Do We Like Conserved Quantities?•5 Minuten
Noether's Theorem•7 Minuten
A Mathematical Trick•8 Minuten
Symmetry in Space Geometry•10 Minuten
The Killing Equation•9 Minuten
The Conserved Quantity Along Geodesic•8 Minuten
Example: Kerr BH Background•11 Minuten
Penrose Process•9 Minuten
Relating to Noether's Theorem•6 Minuten
Lie Derivative•9 Minuten
Recap: Symmetries and Conserved Quantities•3 Minuten
Why Is Action the "First Principle"?•12 Minuten
The Action Principle•7 Minuten
Constructing GR from the First Principle•16 Minuten
Variation Principle of Gravity•12 Minuten
Variation Principle of Matter•12 Minuten
Imposing the Action Principle•10 Minuten
ADM Decomposition•12 Minuten
Are the Two Tensors the Same?•12 Minuten
Recap: The Gravitational Action•1 Minute
How to Study the Cosmic Structures?•9 Minuten
What Physics to Study?•9 Minuten
QFT in Curved Spacetime•8 Minuten
Spectator Field in de Sitter Space•12 Minuten
Solution Under Uncertainty Principle•9 Minuten
Assumption of the Initial State•9 Minuten
How to Understand the "Frozen Nonzero"?•12 Minuten
How to Study the Statistics of the Galaxy Distribution?•12 Minuten
Recap: Origin of Structure from Cosmic Inflation•6 Minuten
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