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Tensor calculus (tensor analysis) is a systematic extension of vector calculus to multivector and tensor fields in a form that is independent of the choice of coordinates on the relevant manifold, but which accounts for respective sub-spaces, their symmetries, and their connections.
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Field equation of Palatini f(R) gravity
I've been reading a paper about a Palatini formulation of f(R,T) gravity theory, and when they vary the gravitational action with respect the connection ˜Γ, they obtain that \begi …
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About variation of Ricci tensor
I have been doing some calculation on variation of Ricci's tensor with respect to the metric, that, according with S. Carroll (An Introduction to General Relativity: Spacetime and Geometry, equation 4 …