General Covariance in Gravity

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Scalar, Vector or Tensor? Gravity

Discusses defining tensors, space-time dimensionality, and challenges in formulating a relativistic theory of gravity.

Special and General Relativity

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Gravitational Field Equations

Covers the formulation of gravitational field equations and the motion of particles in gravitational fields.

Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Curved Space-Time

Discusses curved space-time, arguments against scalar gravity, and relativistic effects of motion.

General Covariance in Gravitational Field

Explores general covariance, Riemann tensor, Bianchi identities, and Einstein tensor in gravitational field.

Einstein Equations

Covers the derivation of Einstein equations and the Schwarzschild metric.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

Scalar Gravity: Einstein Equations

Introduces scalar gravity, covering covariant derivatives, Ricci tensor, Einstein Equivalence Principle, and the generalization of Newtonian gravity equations.