Christoffel Symbols and Gravity Before Einstein

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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.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Material Point Model: Basics

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

Gravitational Field Equations

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

Tensor Analysis: Coordinate Systems

Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

General Covariance in Gravity

Explores general covariance in gravity, covering equations, curvature tensor, and static gravity field.

Special Relativity

Covers the main points of special relativity, including symmetries, transformations, 4-vectors, Maxwell equations, and proper time.

Gravity and Motion

Explores force of motion, dimensions, gravity, tensor fields, and equivalence principle.

Flat Space-Time: Conditions and Theorems

Covers the necessary conditions and theorems to have flat space-time and discusses the symmetry properties of the Riemann tensor.