Einstein's General Relativity and Gravitation

Video Lectures

Displaying all 24 video lectures.
Lecture 1
Introduction
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Introduction
Topics covered: A Brief History of Gravity, Gravity from the Ancient Greeks to Einstein's Relativistic Theory (1907).

Recorded April 1, 2014.

I. Special Relativity
Lecture 2
Review of Lorentz Transformations, Energy, and Momentum
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Review of Lorentz Transformations, Energy, and Momentum
Special Relativity - Part 1 Topics covered: Lorentz Transformations, Euclidean vs. Lorentzian Signature, Proper time. Flat metric, Time dilation, Energy and Momentum, Four-force and Relativistic Equations of Motion. Recorded April 3, 2014.
Lecture 3
Tensor Algebra & Covariant Form of Maxwell's Equations
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Tensor Algebra & Covariant Form of Maxwell's Equations
Special Relativity - Part 2 Topics covered: Four-vectors and Tensors. Covariant and Contravariant Forms. Tensor algebra. Covariant form of Maxwell's Equations. Conservation Laws. Energy-Momentum Tensor. Recorded April 8, 2014.
Lecture 4
Angular Momentum & Relativistic Hydrodynamics
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Angular Momentum & Relativistic Hydrodynamics
Special Relativity - Part 3 Topics covered: Angular Momentum and Spin. Conservation Laws. Relativistic Hydrodynamics. Perfect Fluid. Possible Equations of State. Irreducible Representations of the Lorentz Group. Allowed Values for the Quantum Spin. Recorded April 10, 2014.
II. General Relativity
Lecture 5
Equivalence Principle & Metric Tensors
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Equivalence Principle & Metric Tensors
General Relativity - Part 1 Topics covered: Non-Relativistic (Newtonian) Gravity, Freely Falling Observers, Principle of Equivalence, Statement of the Principle, Supporting Measurements (Eötvös Experiment), Equation of Free Fall (Geodesic Equation), Metric Tensor and Affine Connection. Recorded April 15, 2014.
Lecture 6
Newtonian Limit & Gravitational Red Shift
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Newtonian Limit & Gravitational Red Shift
General Relativity - Part 2 Topics covered: Proper Time and the Derivation of the Equation of Free Fall from a Variational Principle. Significance for the Quantum Mechanical Feynman Path Integral. Newtonian Limit. Time Dilation and Gravitational Red Shift. Order of Magnitude Estimates. Recorded on April 17, 2014.
Lecture 7
General Relativity Time Dilation Effects in GPS Systems.
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General Relativity Time Dilation Effects in GPS Systems.
General Relativity - Part 3 Topics covered: Precision Test of the Equivalence Principle. GR Time Dilation Effects in GPS Systems. Searches for a Possible Anisotropy of Inertia. Equation of Free Fall compared to Newton's Equation. Electromagnetic Analogy (Lorentz Force). The Scale of Time and the Magnitude of the Metric. Asymptotically Flat Metrics as Idealizations. Role of Mach's Principle and the Origin of G. Simple Examples of Coordinate Systems. Coordinate Dependence of the Affine Connection. Recorded on April 22, 2014.
Lecture 8
General Covariance & Affine Connection
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General Covariance & Affine Connection
General Relativity - Part 4 Topics covered: Principle of General Covariance. Local versus Global Invariances, Gauge Fields and the QED Analogy, General Structure of Invariant Equations, Tensor Algebra, Raising and Lowering of Indices, Contractions, Tensor Densities, Space-Time Volume Element, Transformation Properties of the Affine Connection, General Coordinate Invariance of the Equation of Free Fall. Recorded April 24, 2014.
Lecture 9
Covariant Derivatives, Curls and Divergences
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Covariant Derivatives, Curls and Divergences
General Relativity - Part 5 Topics covered: Covariant Derivative, Covariant Derivative of the Metric, Covariant Differentiation along a Path, Examples of Parallel Transports for a Vector, Covariant Curls and Divergences, Finite Parallel Transports with Path Ordered Products, Gauge Invariance and Covariant Derivative in QED. Recorded April 29, 2014.
Lecture 10
Fermi-Walker Transport & Riemann Curvature Tensor
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Fermi-Walker Transport & Riemann Curvature Tensor
General Relativity - Part 6 Topics covered: Particle Mechanics in the Presence of Gravity. Fermi-Walker Transport. Electrodynamics in Covariant Form. Conserved Energy-Momentum Tensor. Hydrodynamic Equations for a Perfect Fluid. Riemann Curvature Tensor. Parallel Transport Around an Infinitesimal Closed Loop. Gravitation versus Curvilinear Coordinates. Algebraic Properties of the Riemann Tensor. Differential (Bianchi) Identities.
III. Einstein's Field Equations
Lecture 11
Derivation of the Einstein Field Equations
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Derivation of the Einstein Field Equations
Einstein's Field Equations - Part 1 Topics covered: Derivation of the Einstein Field Equations. Requirement of General Covariance, Nonrelativistic Limit. Equivalent Forms for the Field Equations. Vacuum Solutions. Cosmological Constant Term. Modifications to Newtonian Gravity. Cosmological Constant Interpreted as a Vacuum Energy. Recorded May 06, 2014
Lecture 12
Einstein-Hilbert Action & Brans-Dicke Theory
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Einstein-Hilbert Action & Brans-Dicke Theory
Einstein's Field Equations - Part 2 Topics covered: Einstein-Hilbert Action, Variational Principle, Palatini Identity. Role of the Action in Constructing the Feynman Path Integral for Quantized Gravity. Gravitational Functional Measure. Need to Maintain General Covariance. Scalar-Tensor Extensions of Gravity. Brans-Dicke Theory. Field Equation Modifications from the Massless BD Scalar. Recorded May 08, 2014.
Lecture 13
Field Equations for a Static Isotropic Metric
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Field Equations for a Static Isotropic Metric
Einstein's Field Equations - Part 3 Topics covered: Field Degrees of Freedom and Constraints. Coordinate Conditions. Analogy to Gauge Choice in Electrodynamics. Physical Degrees of Freedom. Harmonic Gauge. Weak Field Expansion, Linear Part of the Ricci Tensor. Asymptotically Flat Metrics. Energy, Momentum and Angular Momentum of a Gravitational Field. Static Isotropic Metric. Derivation of the Solution to the Field Equations for a Static Isotropic Metric. Recorded May 13, 2014.
IV. Solutions to the Field Equations
Lecture 14
Schwarzschild Solution & Astrophysical Black Holes
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Schwarzschild Solution & Astrophysical Black Holes
Solutions to the Field Equations - Part 1 Topics covered: Schwarzschild Solution. Gravitational Redshift near the Horizon. Coordinate Dependence of Horizon. Kruskal Coordinates. Stationary versus Freely Falling Observers. Kruskal Diagram.The Metric Inside a Star. Astrophysical Black Holes. Equations of Motion for a Particle in the Schwarzschild Metric. Integrals of the Motion. Radial Equation and Effective Potential. Recorded May 15, 2014.
Lecture 15
Photon Orbits in the Schwarzschild Metric
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Photon Orbits in the Schwarzschild Metric
Solutions to the Field Equations - Part 2 Topics covered: Equations for Orbits, Relativistic Correction to the Newtonian Potential, Precession of the Perihelion of Mercury, Celestial Reference Frames, Photon Orbits in the Schwarzschild Metric, Deflection of Light by the Sun, Radar Echo Delay, Robertson Expansion, Present Status of Solar System Tests of General Relativity. Recorded May 20, 2014.
Lecture 16
Weak and Strong Gravitational Fields
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Weak and Strong Gravitational Fields
Solutions to the Field Equations - Part 3 Topics covered: Weak and Strong Gravitational Fields, The Weak Field Expansion, Choice of Background Metric, Linear Part of the Ricci Tensor, Local Gauge Invariance, Gauge Conditions, Wave Equation and Explicit Solution in Terms of Retarded Potentials, Plane Wave Solution, Polarization Amplitudes, Transverse Traceless Modes as Physical Modes, Spin Two of the Graviton. Recorded May 22, 2014.
Lecture 17
Generation and Detection of Gravitational Waves
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Generation and Detection of Gravitational Waves
Solutions to the Field Equations - Part 4 Topics covered: Polarization States for a Gravitational Wave, Generation of Gravitational Waves, Far Field Limit, Expansion in Fourier Components, Angular Dependence of Power Radiated, Quadrupole Radiation, Total Power Emitted, Gravitational Waves Emitted by a Rotating Body, Detection of Gravitational Waves, Bar Detectors and Large Interferometer Detectors. Recorded May 27, 2014.
Lecture 18
Lense-Thirring Effect & Mach's Principle
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Lense-Thirring Effect & Mach's Principle
Solutions to the Field Equations - Part 5 Topics covered: Lense-Thirring Effect and Mach's Principle, Solution of the Field Equations for a Thin Rotating Spherical Shell, Strong Field Case as Obtained from the Kerr Solution, Newton's Constant and Mass Distribution in the Universe, Field Equations Relevant for Cosmology, Assumption of Homogeneity and Isotropy for the Universe, Friedman-Robertson-Walker Metric, Structure of the Field Equations for a Perfect Fluid. Recorded May 29, 2014.
Lecture 19
Field Equations for a Homogeneous Isotropic Metric
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Field Equations for a Homogeneous Isotropic Metric
Solutions to the Field Equations - Part 6 Topics covered: Solutions to the Field Equations for a Homogeneous Isotropic Metric, Relation to Newtonian Mechanics, Matter Dominated Universe, Effects of Radiation and of the Cosmological Constant, Density and Pressure of the Present Universe, Evolution of the Black Body Temperature, Estimates for the Hubble Constant, Relative Contributions of Vacuum Energy and Matter in the Present Universe. Recorded June 03, 2014.
V. Gravitation and Quantum Mechanics
Lecture 20
Gravitons & Quantum-Mechanical Field Fluctuations
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Gravitons & Quantum-Mechanical Field Fluctuations
Topics covered: Gravitational Field as a Collection of Gravitons, Quantum-Mechanical Field Fluctuations, The Path Integral Approach to Gravity and the Need to Retain General Covariance, DeWitt's Functional Measure over Metrics, Feynman's Derivation of the Field Equations for Gravity from the Construction of a Lagrangian for a Massless Spin-Two Particle, Nonlinear Terms due to the Graviton's own Energy and Momentum, Short Distance Modifications to Gravity due to Radiative Corrections. Recorded June 05, 2014.
VI. Student Presentations
Lecture 21
Presentations: Kerr Metric, Gravitational Lensing, GW Detection
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Presentations: Kerr Metric, Gravitational Lensing, GW Detection
Student Presentations - Group 1: - Benjamin Boizelle: Kerr Solution for a Rotating Black Hole - Anna Kwa: Gravitational Lensing - Christopher Persichilli: Gravitational Wave Generation and Detection - Nicolas Canac - Frame Dragging for Satellites
Lecture 22
Presentations: Positive Energy Theorem & Curvature
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Presentations: Positive Energy Theorem & Curvature
Student Presentations - Group 2: - Yucheng Ji: Positive Energy Theorem in GR - James Asbrock: Curvature in D=2,3,4 and Higher Dimensions - Andrew Yang: Two-Dimensional Gravity Recorded June 11, 2014.
Lecture 23
Presentations: Dark Matter, MOND, & Cosmological Inflation
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Presentations: Dark Matter, MOND, & Cosmological Inflation
Student Presentations - Group 3: - Andrew Pace: MOND (Modified Newtonian Mechanics) and GR - Craig Pitcher: Dark Matter Candidates (Neutrinos, Machos, Wimps etc.) - Anthony DiFranzo: Hierarchy Problem and the Planck Mass - Mohammad Abdullah: Cosmological Inflation Recorded June 11, 2014.
Lecture 24
Presentations: Kaluza-Klein Theory & Diagrams for Quantum Gravity
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Presentations: Kaluza-Klein Theory & Diagrams for Quantum Gravity
Student Presentations - Group 4: - Meghan Frate: Higher Dimensional Gravity (Kaluza-Klein Theory) - Jennifer Rittenhouse West: Curvature Squared (R+R^2) Gravity - Aaron Soffa: Tetrad (Vierbein) Formalism and the Planck Mass - Michael Gordon: Feynman Rules and Diagrams for Quantum Gravity

Recorded June 11, 2014.