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General Relativity II: Applications · LearnSpace
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General Relativity II: Applications

Курс от The Hong Kong University of Science and Technology
Уровень не указан≈ 25.6 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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.

Навыки, которые вы освоите

PhysicsApplied MathematicsMechanicsAdvanced MathematicsPhysical ScienceCalculusScientific MethodsMathematical ModelingDifferential EquationsIntegral CalculusLinear Algebra

Программа курса

6 модулей · 175 учебных материалов

01Spherical Solution in the Vacuum & Observational Tests30 материалов

Introduction

What Solutions Do We Care About?Видео

Spherical Symmetric Vacuum Solution

Observational TestsВидеоThe Metric in Spherical SymmetryВидеоSimplifications by Coordinate TransformationsВидео

Учитесь у экспертов

Yi Wang

Professor

General Relativity II: Applications
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Обучение на Coursera

≈ 25.6 ч

6 модулей

Язык: Английский

Субтитры: Дари, Пушту

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Solving RВидео
What If the Sun Suddenly Disappears?Видео
Spherical Symmetric Vacuum SolutionЗадание

Parameterization to Test GR

Parameterization to Test GRВидео

Geodesics of Test Particles

SetupВидеоSimplifying Geodesic Equation 1ВидеоSimplifying Geodesic Equation 2 & 3ВидеоNormalizing λВидеоGeodesics of Test ParticlesЗадание

Orbits of Test Particles and Light

Shape of OrbitsВидеоUnbound OrbitsВидеоHow to Observe?ВидеоBlack Hole ImagingВидеоGravitational LensingВидеоRecap: Geodesics & Orbits of Test ParticlesВидеоBound OrbitsВидеоMercury PrecessionВидеоOrbits of Test Particles and LightЗадание

Time Dilation & Delay Effects

Time DialationВидеоWho Gets Old Faster?ВидеоShapiro DelayВидеоEffective 1D ProblemВидеоFor Newtonian & GR CasesВидеоTime Dilation & Delay EffectsЗадание

Summary

SummaryВидеоRemaining QuestionsВидео
02Stars and Gravitational Collapse13 материалов

Introduction

What to Study About Stars?Видео

A Spherical Star in GR

How to Model Gravity & Matter?ВидеоEinstein's Equations in Both SidesВидеоSolving the Coupled SystemВидеоA Spherical Star in GRЗадание

White Dwarfs and Neutron Stars

Degeneracy Pressure of FermionsВидеоCalculating the PressureВидеоWhite Dwarfs: Low Mass LimitВидеоIs GR Important for White Dwarfs?ВидеоHigh Mass Limit & Neutron StarsВидеоWhite Dwarfs and Neutron StarsЗадание

Limit of Stars and Gravitational Collapse

Recap: Pressure vs. CollapseВидеоLimit of StarsВидео
03Black Holes34 материалов

Introduction

What's the Metric Outside & Inside the Shell?ВидеоRedshift at R=2GMВидеоIs a Black Hole "Black"?ВидеоDoes the Black Hole "Remember"?ВидеоWhere Does Information Go？ВидеоEntropy of Black HolesВидеоAre Fundamental Particles Black Holes?Видео

Schwarzschild Black Holes

Approaching the HorizonВидеоAcross the HorizonВидеоTortoise CoordinatesВидеоEddington-Finkelstein CoordinatesВидеоKruskal CoordinatesВидеоLight Cones in T-R CoordinateВидеоTo the End of the World

Penrose Diagrams

Mapping Infinity to a Finite RangeВидеоPenrose Diagrams of Minkowski SpacetimeВидеоRecap: Schwarzschild Black HolesВидеоRecap: Kruskal CoordinatesВидеоRecap: Penrose DiagramsВидеоPenrose Diagrams of Eternal Black HolesВидео

Reissner-Nordstrom Black Holes

The Metric of RN Black HolesВидеоHorizons of RN Black HolesВидеоExtremal RN Black HolesВидеоRecap: Penrose Diagrams & RN Black HolesВидео

Kerr Black Holes

The Kerr MetricВидеоStationary Solution & SingularityВидеоEvent Horizon of the Kerr MetricВидеоFrame Dragging EffectВидеоInfinite Redshift SurfaceВидеоExtracting Energy from Black HolesВидео

Summary

SummaryВидео
04Gravitational Waves23 материалов

Introduction

Why Should There Be Gravitational Waves?ВидеоWhat to Study for Gravitational Waves?ВидеоGauge of Gauge TheoryВидеоCoulomb Gauge for E&MВидеоLorenz Gauge for E&MВидеоCoulomb Gauge for GravityВидеоGauge ConditionЗадание

Linearized Gravity: Gauge & Wave Equations & Vacuum Solutions

Linearization of RВидеоGauge InvarianceВидеоChoosing de Donger GaugeВидеоDegrees of Freedom for Gravitational WavesВидеоPropagation of Gravitational WavesВидео

Detection of Gravitational Waves

Geodesic Equation for Free ParticlesВидеоAre the Metric Changes Observable?ВидеоGravitational Wave EventsВидеоRecap: Linearization & DetectionВидеоDetection of Gravitational WavesЗадание

Production of Gravitational Waves

Linearized Einstein Equations with MatterВидеоSolution Using the Retarded Green's FunctionВидеоFor Observers Far AwayВидеоQuadrupole Formula of GR RadiationВидеоGravitational Waves from a Binary SystemВидео

Summary

SummaryВидео
05Cosmology28 материалов

General Principles

Is Cosmology a Natural Science?ВидеоRadiation Dominated UniverseВидеоMatter Dominated UniverseВидеоWhere to Start to Study the Universe?ВидеоRecap: History of the UniverseВидеоThe Cosmological PrincipleВидео3D Spaces Satisfying the PrincipleВидеоGeneral Principles of CosmologyЗадание

Matter in the Expanding Universe

Light in the Expanding UniverseВидеоPerfect Fluid in the Expanding UniverseВидеоSolving Continuity EquationВидеоNewtonian Understanding of the Expansion with MatterВидеоRadiation, Matter & Dark Energy Dominated UniversesВидеоMatter in the Expanding UniverseЗадание

Expansion of the Universe

The Friedmann EquationВидеоNewtonian Understanding of the Expansion with Pressureless MatterВидеоRecap: The Cosmological Principle & Expansion of the UniverseВидеоThe Expansion History with ω as ConstantsВидеоAge of the Universe Dominated by Matter & RadiationВидеоAge of the Universe Considering Dark EnergyВидео

Inflationary Cosmology

How to Solve the Horizon Problem?ВидеоInflation Driven by a Scalar FieldВидеоDynamics of the Slow-roll InflationВидеоInflationary CosmologyЗадание

Summary

SummaryВидео
06Selected "Advanced" Topics47 материалов

The Raychaudhuri Equation

Question: Why Is Gravity Attractive?ВидеоConstructing Separation VectorsВидеоSpeed of Spatial Distances Between GeodesicsВидеоAcceleration of Spatial Distances Between GeodesicsВидеоDecompositionВидеоRotation & Expansion ScalarВидеоStrong Energy ConditionВидеоWeak & Null Energy ConditionВидеоRecap: The Raychaudhuri EquationВидео

Symmetries and Conserved Quantities

Why Do We Like Conserved Quantities?ВидеоNoether's TheoremВидеоA Mathematical TrickВидеоSymmetry in Space GeometryВидеоThe Killing EquationВидеоThe Conserved Quantity Along GeodesicВидео

The Gravitational Action

Why Is Action the "First Principle"?ВидеоThe Action PrincipleВидеоConstructing GR from the First PrincipleВидеоVariation Principle of GravityВидеоVariation Principle of MatterВидеоImposing the Action PrincipleВидео

Origin of Structure from Cosmic Inflation

How to Study the Cosmic Structures?ВидеоWhat Physics to Study?ВидеоQFT in Curved SpacetimeВидеоSpectator Field in de Sitter SpaceВидеоSolution Under Uncertainty PrincipleВидеоAssumption of the Initial StateВидео

Quantum Gravity

Can Gravity Remain Classical?ВидеоQM vs. GRВидеоPerturbative Quantization of GravityВидеоNon-renormalizability of GravityВидеоIs Non-renormalizability a Problem?ВидеоThe Planck ScaleВидеоTowards a Theory of Everything
Видео
Do White Holes Exist in Our Universe?Видео
Schwarzschild Black HolesЗадание
Cut & Paste of Penrose DiagramsВидео
Causal Structure of the UniverseВидео
The Old Horizon ProblemВидео
The New Horizon ProblemВидео
Example: Kerr BH BackgroundВидео
Penrose ProcessВидео
Relating to Noether's TheoremВидео
Lie DerivativeВидео
Recap: Symmetries and Conserved QuantitiesВидео
ADM DecompositionВидео
Are the Two Tensors the Same?Видео
Recap: The Gravitational ActionВидео
How to Understand the "Frozen Nonzero"?Видео
How to Study the Statistics of the Galaxy Distribution?Видео
Recap: Origin of Structure from Cosmic InflationВидео
Видео
Disasters of String TheoryВидео
Recap: Quantum GravityВидео