Video Lectures

181 videos covering General Relativity — from introductions to advanced field equations

Curated from eigenchris, Physics for Students, and more

Einstein's Original GR Papers — Full Playlist (17 lectures)

1Featured: General Relativity Overview(2 videos)

General Relativity

Featured

Computers, Geometry and Einstein — Jason Lotay

Geometry & GR

2Advanced General Relativity — Lorentzian Geometry (Lectures 1–5)(5 videos)

Lecture 1: Basics of Lorentzian Geometry

Lorentzian Geometry

Lecture 2: Local Lorentz Frames, Fermion-Gravity Coupling, Isometries

Lorentz Frames

Lecture 3: Geodesics and Geodesic Congruences

Geodesic Congruences

Lecture 4: Raychaudhuri Equation, Geodesic Deviation

Raychaudhuri

Lecture 5: Null Geodesics, Synchronous Coordinates

Null Geodesics

3Advanced GR — Maximally Symmetric Spacetimes (Lectures 6–8)(3 videos)

Lecture 6: Minkowski and Rindler Spacetimes, Penrose Diagrams

Penrose Diagrams

Lecture 7: de Sitter Spacetime

de Sitter

Lecture 8: Anti-de Sitter Spacetime

Anti-de Sitter

4Advanced GR — Causality & Global Structure (Lectures 9–13)(5 videos)

Lecture 9: Causality — Chronological and Causal Future/Past

Causality

Lecture 10: Achronality, Domain of Dependence

Achronality

Lecture 11: Cauchy Surfaces and Globally Hyperbolic Spacetimes

Cauchy Surfaces

Lecture 12: Properties of Globally Hyperbolic Spacetimes

Global Hyperbolicity

Lecture 13: More Properties of Globally Hyperbolic Spacetimes

Global Hyperbolicity

5Advanced GR — Schwarzschild Black Holes (Lectures 14–18)(5 videos)

Lecture 14: Schwarzschild Metric, Birkhoff Theorem

Birkhoff Theorem

Lecture 15: More on Schwarzschild, Proof of Birkhoff Theorem

Birkhoff Proof

Lecture 16: Event Horizon, Maximally Extended Black Hole

Kruskal Extension

Lecture 17: What We Learn from Kruskal Coordinates

Kruskal Coordinates

Lecture 18: Killing Horizons and Surface Gravity

Surface Gravity

6Advanced GR — Singularity Theorems (Lectures 19–23)(5 videos)

Lecture 19: More on Surface Gravity; Geodesics and Focal Points

Focal Points

Lecture 20: Covariant Description of Geodesic Focusing

Geodesic Focusing

Lecture 21: Hawking’s Singularity Theorem

Hawking Theorem

Lecture 22: Promptness and Achronality for Causal Curves

Causal Curves

Lecture 23: Penrose Singularity Theorem

Penrose Theorem

7Advanced GR — Black Hole Thermodynamics (Lectures 24–27)(4 videos)

Lecture 24: Asymptotically Flat Spacetimes and Generic Black Holes

Asymptotic Flatness

Lecture 25: Trapped Surfaces, Hawking Area Theorem

Area Theorem

Lecture 26: Mass and Angular Momentum, BH Thermodynamics

BH Thermodynamics

Lecture 27: Smarr Formula and Laws of BH Thermodynamics

Smarr Formula

8Introduction & History of General Relativity(11 videos)

Introduction to General Relativity

Introduction

Introduction to General Relativity for Beginners

Introduction

General Relativity Introduction — Lecture

Introduction

General Relativity for Beginners — Lecture Series

Beginners

General Relativity for Beginners — General Theory

Beginners

History of General Relativity

History

History of General Relativity — How GR Was Discovered

History

How to Learn General Relativity

Study Guide

How to Learn & Understand General Relativity

Study Guide

How to Learn General Relativity — Roadmap

Study Guide

Leonard Susskind on General Relativity

Susskind

9Special Relativity & Minkowski Space(4 videos)

Special Theory of Relativity — Lecture

Special Relativity

General Relativity — From Special Relativity to Field Equations

Special Relativity

Minkowski Space & Spacetime Explained — Light Cone

Minkowski Space

Time Dilation Explained — Why Time Slows Down

Time Dilation

10Tensor Calculus & Differential Geometry(4 videos)

Tensor Calculus for General Relativity

Tensor Calculus

Tensor Calculus — Metric Tensor & Cylindrical Coordinates

Metric Tensor

Metric Tensor — What Is a Metric Tensor in GR

Metric Tensor

Christoffel Symbols — General Relativity Lecture

Christoffel Symbols

11Curvature — Ricci Tensor & Riemann Tensor(4 videos)

Ricci Tensor, Ricci Scalar, Stress Energy & Einstein Tensor

Curvature Tensors

Ricci Tensor & Stress Energy Tensor — Detailed Lecture

Curvature Tensors

Ricci Curvature Tensor & Einstein Field Equations

Ricci Tensor

Ricci Curvature Tensor — General Relativity Lecture

Ricci Tensor

12Geodesics & How Gravity Bends Light(4 videos)

Geodesics — Einstein Field Equations Explained

Geodesics

Geodesics in General Relativity

Geodesics

How Gravity Bends Light — General Relativity Lecture

Light Bending

How Gravity Affects the Path of Light

Light Bending

13Einstein Field Equations(9 videos)

What Is a Field Equation — Classical Fields & Path Integral

Field Equations

Einstein Field Equation Explained — For Beginners

EFE Explained

Einstein Field Equations Explained

EFE Explained

Einstein Field Equations — General Theory

EFE

Einstein Field Equations — Detailed Explanation

EFE

Einstein Field Equations — Advanced

EFE

General Relativity & Field Equations Explained

EFE

General Relativity Math — Einstein Field Equations

EFE Math

General Relativity Mathematics Explained

GR Math

14Einstein-Hilbert Action(1 videos)

Einstein-Hilbert Action Explanation

EH Action

15Black Holes(1 videos)

What Is a Black Hole — General Relativity Lecture

Black Holes

16General Relativity & Quantum Mechanics(1 videos)

General Relativity and Quantum Mechanics

GR & QM

17Full Lecture Series(6 videos)

General Relativity Lecture — Field Equations (Part 1)

Lecture Series

General Relativity Lecture — Field Equations (Part 2)

Lecture Series

General Theory of Relativity — Full Lecture

Lecture Series

General Theory of Relativity — Explained

Lecture Series

General Theory of Relativity — Lecture Series

Lecture Series

General Theory of Relativity — Lecture

Lecture Series

18Relativity by eigenchris — Galilean & Special Relativity(15 videos)

Relativity 101a: Introduction to Galilean Relativity

Galilean Relativity

Relativity 101b: Introduction to Special Relativity

Special Relativity

Relativity 102a: Keys to Relativity Math — Invariance

Math Foundations

Relativity 102b: Keys to Relativity — Covariance and Contravariance

Math Foundations

Relativity 103a: Galilean Relativity — Spacetime Diagrams

Spacetime Diagrams

Relativity 103b: Galilean Relativity — Spacetime Separation Vector

Spacetime Intervals

Relativity 103c: Galilean Relativity — Galilean Transform & Covariance

Galilean Transform

Relativity 103d: Galilean Relativity — Euclidean Metric Tensor

Metric Tensor

Relativity 103e: Galilean Relativity — Problems with Galilean Relativity

Galilean Problems

Relativity 104a: Special Relativity — Lorentz Transform Geometry

Lorentz Transform

Relativity 104b: Special Relativity — Lorentz Transform Equations

Lorentz Transform

Relativity 104c: Special Relativity — Time Dilation & Length Contraction

Time Dilation

Relativity 104d: Special Relativity — Velocity Addition & Simultaneity

Velocity Addition

Relativity 104e: Special Relativity — Spacetime Interval & Minkowski Metric

Minkowski Metric

Relativity 104f: Special Relativity — Relativistic Dynamics & 4-Vectors (E=mc²)

4-Vectors

19Relativity by eigenchris — Acceleration & Rindler Coordinates(7 videos)

Relativity 105a: Hyperbolic Motion and Rindler Horizon

Rindler Coordinates

Relativity 105b: Bell's Spaceship Paradox & Rindler Coordinates

Rindler Coordinates

Relativity 105c: The Jacobian — Changing Basis in Curvilinear Coordinates

Jacobian

Relativity 105d: Twin Paradox & Proper Time Along Curves (Rindler Metric)

Twin Paradox

Relativity 105e: Covariant Derivative in Flat Spacetime (Rindler)

Covariant Derivative

Relativity 105f: Geodesics & Curved Light Beams (Rindler Coordinates)

Geodesics

Relativity 106a: Frequency Wave Covectors & Doppler Shift

Covectors

20Relativity by eigenchris — General Relativity Basics(6 videos)

Relativity 107a: GR Basics — Equivalence Principle & Acceleration

Equivalence Principle

Relativity 107b: GR Basics — Manifolds, Covariant Derivative, Geodesics

Manifolds

Relativity 107c: GR Basics — Curvature, Riemann, Ricci Tensor, Ricci Scalar

Curvature

Relativity 107d: GR Basics — Curved Spacetime for Newtonian Gravity

Newtonian Limit

Relativity 107e: GR Basics — Stress-Energy-Momentum Tensor

Stress-Energy Tensor

Relativity 107f: GR Basics — Einstein Field Equation Derivation

EFE Derivation

21Relativity by eigenchris — Schwarzschild Metric & Black Holes(5 videos)

Relativity 108a: Schwarzschild Metric — Derivation

Schwarzschild

Relativity 108b: Schwarzschild Metric — Gravitational Time Dilation, Event Horizon

Event Horizon

Relativity 108c: Schwarzschild Geodesics — Mercury Perihelion, Photon Sphere

Geodesics

Relativity 108d: Schwarzschild — Eddington-Finkelstein, Kruskal-Szekeres

Coordinates

Relativity 108e: Schwarzschild — Gravitational Redshift/Blueshift

Redshift

22Relativity by eigenchris — Gravitational Waves(5 videos)

Relativity 109a: Gravitational Waves — Introduction (LIGO, Wave Equation)

GW Introduction

Relativity 109b: Gravitational Waves — Linearized / Weak Gravity

Linearized Gravity

Relativity 109c: Gravitational Waves — Wave Derivation (Lorenz Gauge)

Wave Derivation

Relativity 109d: Gravitational Waves — TT Gauge (Plus & Cross Polarizations)

Polarizations

Relativity 109e: Gravitational Waves — How GWs Affect Particles (Geodesic Deviation)

Geodesic Deviation

23Relativity by eigenchris — Cosmology(6 videos)

Relativity 110a: Cosmology — Introduction to Modern Cosmology

Introduction

Relativity 110b: Cosmology — FLRW Metric Derivation (3 Geometries)

FLRW Metric

Relativity 110c: Cosmology — FLRW Tensor/Coefficient Derivations

FLRW Tensors

Relativity 110d: Cosmology — FLRW Geodesics, Redshift, Horizons, Comoving

Cosmological Redshift

Relativity 110e: Cosmology — Perfect Fluids, Equation of State

Perfect Fluids

Relativity 110f: Cosmology — Friedmann Equations & Universe Evolution (FINALE)

Friedmann Equations

24En français(7 videos)

Pourquoi la gravité n’est pas une force

Gravité

Calcul tensoriel pour la relativité générale

Calcul tensoriel

Introduction à la relativité générale

Introduction

Théorie de la relativité générale — Cours 1

Cours

Théorie de la relativité générale — Cours 2

Cours

Explication de l’action d’Einstein-Hilbert

Action EH

Explication des trous noirs — Relativité générale

Trous noirs

25Advanced General Relativity (24 Lectures)(24 videos)

Lecture 1

Foundations

Lecture 2

Foundations

Lecture 3

Foundations

Lecture 4

Foundations

Lecture 5

Foundations

Lecture 6

Curvature

Lecture 7

Curvature

Lecture 8

Curvature

Lecture 9

Einstein Eq.

Lecture 10

Einstein Eq.

Lecture 11

Einstein Eq.

Lecture 12

Schwarzschild

Lecture 13

Schwarzschild

Lecture 14

Schwarzschild

Lecture 15

Kerr

Lecture 16

Kerr

Lecture 17

Kerr

Lecture 18

Cosmology

Lecture 19

Cosmology

Lecture 20

Cosmology

Lecture 21

Lecture 22

Lecture 23

Lecture 24

Advanced

26Einstein's Original GR Papers — Lecture by Lecture(17 videos)

How Einstein shows the inverse of the metric tensor is a tensor

Metric Tensor

How Einstein found an invariant volume element

Volume Element

How Einstein derives the geodetic line equation

Geodesic Equation

How Einstein derives the covariant derivative

Covariant Derivative

Rule of differentiation of determinants

Determinants

How Einstein derives the covariant divergence

Covariant Divergence

Other important tensor expressions

Tensor Expressions

How Einstein derives the Riemann tensor

Riemann Tensor

Field equations in the absence of matter

Vacuum Field Equations

Field equations from the variation principle

Variational Principle

Field equations in the presence of matter

Matter Field Equations

Energy tensor of a frictionless adiabatic fluid

Energy Tensor

How Einstein derives Maxwell equations in covariant form

Maxwell Equations

GR reduces to Newtonian physics

Newtonian Limit

Deflection of a light ray due to gravity

Light Deflection

GR from Hamilton's principle

Hamilton Principle

Cosmological considerations

Cosmology

27Additional GR Lecture Series(1 videos)

Additional Lecture

GR Lecture

283D Gravity, Tetrad Formalism & Loop Quantum Gravity (14 Lectures)(14 videos)

Lecture 1: Einstein-Hilbert Action, Einstein’s Theory in 3D

3D Gravity

Lecture 2: Tetrad Formalism, Vielbeins, Torsion

Tetrads

Lecture 3: First Order Formalism, Symmetries

First Order

Lecture 4: Hamiltonian Analysis, Canonical Variables

Hamiltonian

Lecture 5: Constraints, Gauge Transformations

Constraints

Lecture 6: Phase Space, Dirac Observables

Dirac Obs.

Lecture 7: Quantization of Parametrized Particle I

Quantization

Lecture 8: Quantization of Parametrized Particle II

Quantization

Lecture 9: SO(3), SU(2), and Holonomy

Holonomy

Lecture 10: Holonomies, Fluxes, Poisson Algebra

LQG

Lecture 11: Quantization, SU(2) Gymnastics

LQG

Lecture 12: Hilbert Space, Fluxes, Length Quantized

LQG

Lecture 13: Gauss Constraint, Intertwiner

LQG

Lecture 14: Lightning Review of 3+1 LQG

LQG

Additional GR Lecture Series — Full Playlist

Loop Quantum Gravity & Quantum Gravity Lectures

25 lectures from leading researchers: Strominger, Rovelli, Freidel, Bianchi, Perez, Geiller, Agullo, and more.

Full Playlist (25 lectures)

The Infrared Triangle in Quantum Gravity

Andrew Strominger

Black Hole to White Hole Transition

Carlo Rovelli

Introduction to Local Holography

Laurent Freidel

Quantum Information for Quantum Gravity — Lecture 1

Eugenio Bianchi

Quantum Reference Frames

Flaminia Giacomini

QFT in Curved Spacetime — Lecture 1

Ivan Agullo

Classical and Quantum Black Holes — Lecture 1

Alejandro Perez

Symmetries in GR, Conserved Charges, and Edge Modes — Lecture 1

Marc Geiller

LQG, Spin Networks and Spin Foams — Lecture 1

Maïté Dupuis

Gravitational Waves and Prospects for QG

David Nichols

Loops'24 Summer School — Loop Quantum Gravity

27 lectures from the 2024 Loops Summer School: canonical & covariant LQG, spin foams, LQC, BH-to-WH transitions, Regge calculus. Featuring Giesel, Vidotto, Rovelli, Ashtekar, Dittrich, Singh.

Full Playlist (27 lectures)

Introduction to Canonical LQG — Lecture 1

Kristina Giesel

Covariant Loop Quantum Gravity — Lecture 1

Francesca Vidotto

Black Hole to White Hole Transition — Lecture 1

Carlo Rovelli

Black Holes in Loop Quantum Gravity — Lecture 1

Abhay Ashtekar

Loop Quantum Cosmology — Lecture 1

Parampreet Singh

Regge Calculus and Applications to LQG — Lecture 1

Bianca Dittrich

Numerics for Spin Foams — Lecture 1

Hongguang Liu

Spin Foam Model with Cosmological Constant — Lecture 1

Qiaoyin Pan

Understanding Tensor Calculus (22 lectures)

Complete series covering tensors, Christoffel symbols, covariant derivatives, Lie derivatives, Riemann and Ricci tensors, differential forms, and Hodge duality.

Tensors as Maps

Episode 1

The Affine Connection

Episode 5

What Really are Christoffel Symbols?

Episode 6

The Covariant Derivative

Episode 8

The Riemann Curvature Tensor

Episode 13

The Ricci Tensor

Episode 15

Quantum Gravity — From Complex Manifolds to LQG (30 lectures)

Deep dive into quantum gravity: complex manifolds, spinors, tetrads, ADM formalism, Ashtekar variables, and canonical quantisation.

Introducing Loop Quantum Gravity

QG Lecture 1

The Building Blocks: Tetrads!

QG Lecture 6

The ADM Formalism

QG Lecture 8

The "Quantum" Part of Quantum Gravity

QG Lecture 13

Ashtekar's Canonical Variables

QG Lecture 17

A New Understanding of Quantum Gravity

QG Lecture 14

Modern Developments in General Relativity

Lectures from the King's College London conference tracing the modern development of GR from Bondi's group in the 1950s — including Pirani's work on gravitational waves (LIGO foundations), Bondi–Sachs BMS symmetries, Penrose diagrams, Robinson's black hole uniqueness theorem, and Davies–Ford quantum effects in curved spacetimes. Featuring David Robinson, Larry Ford, Roger Penrose, and other distinguished speakers.