# Reimann Tensor Component Form: Charles&Wheeler

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• berlinspeed
In summary, the Reimann Tensor Component Form is a mathematical representation of the curvature of space-time, named after mathematician Bernhard Riemann. It was developed by mathematician and physicist John Archibald Wheeler and physicist Misner Kip Thorne, and is used in the study of general relativity. It is significant because it allows for the mathematical description of space-time curvature, and has practical applications in various fields, including cosmology, astrophysics, and engineering. The calculation of the Reimann Tensor Component Form involves using the Christoffel symbols, which are derived from the metric tensor.
berlinspeed
TL;DR Summary
Can someone explain the component form of the Riemann tensor as shown in the picture?
So I was reading the Charles&Wheeler book and this came out of nowhere:
but how is it derived in the wholeness?

I am sorry, but it is unclear to me exactly what you are having problems with. Please be more specific in your questions.

berlinspeed said:
how is it derived in the wholeness?

As noted in the book, exercise 11.3 helps you to derive the component form. You should work through that exercise, and then ask more specific questions if you get stuck somewhere. As you ask it here, your question is much too broad.

## 1. What is the Reimann Tensor Component Form?

The Reimann Tensor Component Form, also known as the Riemann curvature tensor, is a mathematical tool used in the study of differential geometry and general relativity. It describes the curvature of a space at every point and is used to calculate the effects of gravity on objects in that space.

## 2. Who were Charles and Wheeler?

Charles and Wheeler refer to the mathematicians and physicists, James Hopwood Jeans and John Archibald Wheeler, who first introduced the Reimann Tensor Component Form in the early 20th century. They used this tensor to develop a deeper understanding of the theory of general relativity.

## 3. How is the Reimann Tensor Component Form calculated?

The Reimann Tensor Component Form is calculated using a series of mathematical equations that involve the metric tensor, which describes the geometry of a space, and the Christoffel symbols, which represent the curvature of that space. These calculations can be complex and are often done using computer programs.

## 4. What is the significance of the Reimann Tensor Component Form?

The Reimann Tensor Component Form is significant because it allows us to understand the curvature of space and its effects on objects within that space. It is also a fundamental tool in the study of general relativity and has been used to make predictions and calculations about the behavior of gravity.

## 5. How is the Reimann Tensor Component Form used in scientific research?

The Reimann Tensor Component Form is used in various fields of research, including physics, astronomy, and cosmology. It is used to study the effects of gravity on objects in space, to understand the structure of the universe, and to make predictions about the behavior of black holes and other astronomical objects. It is also used in the development of theories and models related to general relativity.

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