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In conclusion, GR is a fundamental theory of gravity... the theoretical minimum general relativity pdf
where $\Gamma_{ij}$ are the Christoffel symbols, which describe the connection between nearby points in spacetime. Please let me know if the link does not work
The mathematical framework of GR is based on Riemannian geometry, which describes the curvature of spacetime using the Riemann tensor. The Riemann tensor is a mathematical object that describes the curvature of spacetime at a given point, and is defined as: the theoretical minimum general relativity pdf
The Einstein Field Equations (EFE) are the core of GR, and describe how the curvature of spacetime is related to the mass and energy density of objects. The EFE are a set of 10 non-linear partial differential equations that can be written in the form: