# Covariant Derivation of the Ricci Tensor: Einstein's Method Now Online

• nobraner
In summary, covariant derivation is a mathematical technique used in differential geometry to find the rate of change of a tensor field along a specified direction or path. The Ricci tensor is a symmetric tensor used in general relativity to describe the curvature of spacetime, combining information from the Riemann curvature tensor and the metric tensor. Einstein's method for covariant derivation involves using parallel transport, and it is important in understanding the curvature of spacetime and deriving equations for particles and fields in general relativity. To learn more about this topic, one can study differential geometry and general relativity, utilize online resources and textbooks, and refer to Einstein's online method.
nobraner
The full derivation of the covariant derivative of the Ricci Tensor as Einstein did it, is now available on line at

https://sites.google.com/site/generalrelativity101/appendix-c-the-covariant-derivative-of-the-ricci-tensor

For those who wish to study it.

nobraner, Your expressions all have two lower μ indices, which is incorrect. Would you like to raise one of them by inserting a gμν?

Bill,

Finally found the time to fix this. One of my biggest weaknesses is ignoring the upper/lower covariant derivative convention. I guess I always think of covariant derivatives as always being covariant.

## 1. What is a covariant derivation?

A covariant derivation is a mathematical technique used in differential geometry to find the rate of change of a tensor field along a specified direction or path.

## 2. What is the Ricci tensor?

The Ricci tensor is a mathematical object used in general relativity to describe the curvature of spacetime. It is a symmetric tensor that combines the information from the Riemann curvature tensor and the metric tensor.

## 3. What is Einstein's method for covariant derivation?

Einstein's method for covariant derivation involves using the concept of parallel transport to find the rate of change of a tensor field along a specified direction or path. This method is often used in general relativity to derive the equations of motion for particles and fields.

## 4. Why is the covariant derivation of the Ricci tensor important?

The covariant derivation of the Ricci tensor is important because it allows us to understand the curvature of spacetime, which is a key concept in Einstein's theory of general relativity. This method also helps us to derive important equations that describe the behavior of particles and fields in curved spacetime.

## 5. How can I learn more about the covariant derivation of the Ricci tensor?

You can learn more about the covariant derivation of the Ricci tensor by studying differential geometry and general relativity. There are also many online resources and textbooks available that explain this topic in detail. Additionally, the recently published online method by Einstein is a great resource for understanding this concept.

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