General Relativity II: Applications

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The Hong Kong University of Science and Technology

General Relativity II: Applications

Instructeur : Yi Wang

Inclus avec

6 modules

Obtenez un aperçu d'un sujet et apprenez les principes fondamentaux.

3 semaines à compléter

à 10 heures par semaine

Planning flexible

Apprenez à votre propre rythme

6 modules

Obtenez un aperçu d'un sujet et apprenez les principes fondamentaux.

3 semaines à compléter

à 10 heures par semaine

Planning flexible

Apprenez à votre propre rythme

Compétences que vous acquerrez

Catégorie : Integral Calculus
Catégorie : Linear Algebra
Catégorie : Calculus
Catégorie : Mathematical Modeling
Catégorie : Advanced Mathematics
Catégorie : Physics
Catégorie : Physical Science
Catégorie : Differential Equations
Catégorie : Mechanics
Catégorie : Scientific Methods
Catégorie : Applied Mathematics

Détails à connaître

Certificat partageable

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Évaluations

12 devoirs

Enseigné en Anglais

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Il y a 6 modules dans ce cours

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.

Inclus

26 vidéos4 devoirs

26 vidéosTotal 230 minutes

What Solutions Do We Care About?6 minutes
Observational Tests13 minutes
The Metric in Spherical Symmetry8 minutes
Simplifications by Coordinate Transformations11 minutes
Solving R10 minutes
What If the Sun Suddenly Disappears?3 minutes
Parameterization to Test GR7 minutes
Setup6 minutes
Simplifying Geodesic Equation 111 minutes
Simplifying Geodesic Equation 2 & 35 minutes
Normalizing λ10 minutes
Shape of Orbits6 minutes
Unbound Orbits10 minutes
How to Observe?12 minutes
Black Hole Imaging6 minutes
Gravitational Lensing9 minutes
Recap: Geodesics & Orbits of Test Particles12 minutes
Bound Orbits11 minutes
Mercury Precession7 minutes
Time Dialation13 minutes
Who Gets Old Faster?8 minutes
Shapiro Delay12 minutes
Effective 1D Problem5 minutes
For Newtonian & GR Cases12 minutes
Summary12 minutes
Remaining Questions5 minutes

4 devoirsTotal 25 minutes

Spherical Symmetric Vacuum Solution10 minutes
Geodesics of Test Particles5 minutes
Orbits of Test Particles and Light5 minutes
Time Dilation & Delay Effects5 minutes

Inclus

11 vidéos2 devoirs

11 vidéosTotal 91 minutes

What to Study About Stars?7 minutes
How to Model Gravity & Matter?11 minutes
Einstein's Equations in Both Sides8 minutes
Solving the Coupled System12 minutes
Degeneracy Pressure of Fermions8 minutes
Calculating the Pressure10 minutes
White Dwarfs: Low Mass Limit9 minutes
Is GR Important for White Dwarfs?6 minutes
High Mass Limit & Neutron Stars7 minutes
Recap: Pressure vs. Collapse6 minutes
Limit of Stars8 minutes

2 devoirsTotal 15 minutes

A Spherical Star in GR5 minutes
White Dwarfs and Neutron Stars10 minutes

Inclus

33 vidéos1 devoir

33 vidéosTotal 317 minutes

What's the Metric Outside & Inside the Shell?9 minutes
Redshift at R=2GM12 minutes
Is a Black Hole "Black"?10 minutes
Does the Black Hole "Remember"?10 minutes
Where Does Information Go？11 minutes
Entropy of Black Holes9 minutes
Are Fundamental Particles Black Holes?9 minutes
Approaching the Horizon5 minutes
Across the Horizon9 minutes
Tortoise Coordinates9 minutes
Eddington-Finkelstein Coordinates10 minutes
Kruskal Coordinates10 minutes
Light Cones in T-R Coordinate10 minutes
To the End of the World11 minutes
Do White Holes Exist in Our Universe?9 minutes
Mapping Infinity to a Finite Range7 minutes
Penrose Diagrams of Minkowski Spacetime11 minutes
Recap: Schwarzschild Black Holes10 minutes
Recap: Kruskal Coordinates13 minutes
Recap: Penrose Diagrams9 minutes
Penrose Diagrams of Eternal Black Holes7 minutes
Cut & Paste of Penrose Diagrams12 minutes
The Metric of RN Black Holes9 minutes
Horizons of RN Black Holes13 minutes
Extremal RN Black Holes11 minutes
Recap: Penrose Diagrams & RN Black Holes14 minutes
The Kerr Metric11 minutes
Stationary Solution & Singularity7 minutes
Event Horizon of the Kerr Metric12 minutes
Frame Dragging Effect9 minutes
Infinite Redshift Surface5 minutes
Extracting Energy from Black Holes7 minutes
Summary8 minutes

1 devoirTotal 5 minutes

Schwarzschild Black Holes5 minutes

Inclus

21 vidéos2 devoirs

21 vidéosTotal 162 minutes

Why Should There Be Gravitational Waves?4 minutes
What to Study for Gravitational Waves?12 minutes
Gauge of Gauge Theory12 minutes
Coulomb Gauge for E&M7 minutes
Lorenz Gauge for E&M8 minutes
Coulomb Gauge for Gravity6 minutes
Linearization of R5 minutes
Gauge Invariance9 minutes
Choosing de Donger Gauge7 minutes
Degrees of Freedom for Gravitational Waves5 minutes
Propagation of Gravitational Waves9 minutes
Geodesic Equation for Free Particles9 minutes
Are the Metric Changes Observable?10 minutes
Gravitational Wave Events10 minutes
Recap: Linearization & Detection5 minutes
Linearized Einstein Equations with Matter5 minutes
Solution Using the Retarded Green's Function6 minutes
For Observers Far Away9 minutes
Quadrupole Formula of GR Radiation11 minutes
Gravitational Waves from a Binary System7 minutes
Summary7 minutes

2 devoirsTotal 35 minutes

Gauge Condition30 minutes
Detection of Gravitational Waves5 minutes

Inclus

25 vidéos3 devoirs

25 vidéosTotal 219 minutes

Is Cosmology a Natural Science?14 minutes
Radiation Dominated Universe10 minutes
Matter Dominated Universe8 minutes
Where to Start to Study the Universe?11 minutes
Recap: History of the Universe7 minutes
The Cosmological Principle15 minutes
3D Spaces Satisfying the Principle6 minutes
Light in the Expanding Universe8 minutes
Perfect Fluid in the Expanding Universe11 minutes
Solving Continuity Equation9 minutes
Newtonian Understanding of the Expansion with Matter8 minutes
Radiation, Matter & Dark Energy Dominated Universes6 minutes
The Friedmann Equation5 minutes
Newtonian Understanding of the Expansion with Pressureless Matter12 minutes
Recap: The Cosmological Principle & Expansion of the Universe11 minutes
The Expansion History with ω as Constants8 minutes
Age of the Universe Dominated by Matter & Radiation6 minutes
Age of the Universe Considering Dark Energy9 minutes
Causal Structure of the Universe7 minutes
The Old Horizon Problem9 minutes
The New Horizon Problem7 minutes
How to Solve the Horizon Problem?11 minutes
Inflation Driven by a Scalar Field11 minutes
Dynamics of the Slow-roll Inflation10 minutes
Summary2 minutes

3 devoirsTotal 15 minutes

General Principles of Cosmology5 minutes
Matter in the Expanding Universe5 minutes
Inflationary Cosmology5 minutes

Inclus

47 vidéos

47 vidéosTotal 422 minutes

Question: Why Is Gravity Attractive?9 minutes
Constructing Separation Vectors8 minutes
Speed of Spatial Distances Between Geodesics9 minutes
Acceleration of Spatial Distances Between Geodesics10 minutes
Decomposition9 minutes
Rotation & Expansion Scalar8 minutes
Strong Energy Condition11 minutes
Weak & Null Energy Condition7 minutes
Recap: The Raychaudhuri Equation4 minutes
Why Do We Like Conserved Quantities?5 minutes
Noether's Theorem7 minutes
A Mathematical Trick8 minutes
Symmetry in Space Geometry10 minutes
The Killing Equation9 minutes
The Conserved Quantity Along Geodesic8 minutes
Example: Kerr BH Background11 minutes
Penrose Process9 minutes
Relating to Noether's Theorem6 minutes
Lie Derivative9 minutes
Recap: Symmetries and Conserved Quantities3 minutes
Why Is Action the "First Principle"?12 minutes
The Action Principle7 minutes
Constructing GR from the First Principle16 minutes
Variation Principle of Gravity12 minutes
Variation Principle of Matter12 minutes
Imposing the Action Principle10 minutes
ADM Decomposition12 minutes
Are the Two Tensors the Same?12 minutes
Recap: The Gravitational Action1 minute
How to Study the Cosmic Structures?9 minutes
What Physics to Study?9 minutes
QFT in Curved Spacetime8 minutes
Spectator Field in de Sitter Space12 minutes
Solution Under Uncertainty Principle9 minutes
Assumption of the Initial State9 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 Inflation6 minutes
Can Gravity Remain Classical?10 minutes
QM vs. GR11 minutes
Perturbative Quantization of Gravity11 minutes
Non-renormalizability of Gravity7 minutes
Is Non-renormalizability a Problem?9 minutes
The Planck Scale10 minutes
Towards a Theory of Everything13 minutes
Disasters of String Theory7 minutes
Recap: Quantum Gravity3 minutes

Instructeur

Yi Wang

The Hong Kong University of Science and Technology

5 Cours31 459 apprenants

Offert par

The Hong Kong University of Science and Technology

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