The Mathematics of General Relativity

Introduction: (00:00-01:19)

Chapter 1: Manifolds (00:01:19-00:10:35)
https://dibeos.net/2025/04/12/how-to-get-to-manifolds-naturally/

Chapter 2: How to do Calculus on manifolds (00:10:35-00:19:04)
https://dibeos.net/2025/04/12/how-to-do-calculus-on-an-abstract-manifold/

Chapter 3: What Differential Geometry is all about (00:19:04-00:32:16)
https://dibeos.net/2025/04/12/the-core-of-differential-geometry/

Chapter 4: Tangent spaces in Differential Geometry (00:32:16-00:44:12)
https://dibeos.net/2025/04/12/what-are-tangent-spaces-in-differential-geometry/

Chapter 5: Schwarzschild spacetime (00:44:12-00:54:00)
https://dibeos.net/2025/04/06/the-mathematics-behind-the-schwarzschild-solution/

Chapter 6: What curvature really is (00:54:00-1:11:01)
https://dibeos.net/2025/04/12/the-intuition-behind-curved-spaces/

Chapter 7: The mathematics of Minkowski spacetime (1:11:01-1:33:01)
https://dibeos.net/2025/04/06/the-mathematics-of-minkowski-spacetime/

Chapter 8: Riemannian manifolds (1:33:01-1:46:57)
https://dibeos.net/2025/05/03/riemannian-manifolds-in-12-minutes/

Chapter 9: Gaussian curvature (1:46:57-2:00:34)
https://dibeos.net/2025/05/10/how-to-describe-a-surface-with-2-numbers/

Chapter 10: Ricci curvature tensor (2:00:34-2:10:11)
https://dibeos.net/2025/05/17/how-to-describe-an-entire-space-with-a-matrix-ricci-curvature/

Chapter 11: Scalar curvature (2:10:11-2:22:34)
https://dibeos.net/2025/05/24/how-a-single-real-number-determines-curvature/

Chapter 12: Conformal geometry (2:22:34-2:39:02)
https://dibeos.net/2025/06/07/why-spacetime-isnt-always-curved/

Chapter 13: Metric tensor (2:39:02-2:50:11)
https://dibeos.net/2025/06/21/how-would-you-measure-distances-in-curved-spaces/

Chapter 14: Tensor calculus (2:50:11-3:07:23)
https://dibeos.net/2025/07/05/the-core-of-tensor-calculus/

Chapter 15: Intrinsic curvature (3:07:23-3:19:22)
https://dibeos.net/2025/07/19/what-is-the-universe-expanding-into-according-to-pure-math/

Chapter 16: Differential forms (3:19:22-3:40:04)
https://dibeos.net/2025/08/09/the-core-of-differential-forms/

Chapter 17: Geodesic equation (3:40:04-3:59:05)
https://dibeos.net/2025/09/06/top-5-methods-for-solving-the-geodesic-equation/

Chapter 18: Tensor impostors (3:59:05-4:09:34)
https://dibeos.net/2025/09/13/why-tensor-impostors-fool-so-many-people/

Chapter 19: The right side of Einstein’s equations (4:09:34-4:18:40)
https://dibeos.net/2025/09/20/mathematician-vs-physicist-whats-on-the-right-side-of-einsteins-equation/

Chapter 20: The main solutions to Einstein’s field equations (4:18:40-4:32:57)
https://dibeos.net/2025/10/29/the-main-solutions-of-einstein-field-equations/

Books:

Catalogue of spacetimes:
https://arxiv.org/pdf/0904.4184

General Relativity (Wald):
https://amzn.to/4hAJymk

Gravitation (Misner, Thorne, Wheeler):
https://amzn.to/3WvPAuJ

Spacetime and Geometry: An Introduction to General Relativity (Carroll):
https://amzn.to/4ofaNVU

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