Is there any good reference of tetrad in GR

Thread starter yicong2011
Start date Apr 7, 2011
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Gr Reference Tetrad

In summary, a tetrad in general relativity is a set of four vector fields that span the tangent space of a curved spacetime. It is used to define a local coordinate system and calculate physical quantities. A tetrad differs from a coordinate basis in that its vectors are orthonormal and used for curved spacetimes, while a coordinate basis is used for flat spacetimes. The purpose of using a tetrad is to simplify calculations in general relativity. There are different types of tetrads, such as the orthonormal tetrad, null tetrad, and Newman-Penrose tetrad, each with their own properties and applications. Resources for learning about tetrads in GR include textbooks, online lectures, and research articles,

Apr 7, 2011

yicong2011

I want to find a good reference in GR about the application of tetrad.
Is there any good suggestions?

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Apr 7, 2011

atyy

Science Advisor

Try Winitzki's notes, chapters 6 and 7.3.1

Apr 7, 2011

xienohp

carten, Intro . to spacetime and geometry, appendix

Related to Is there any good reference of tetrad in GR

1. What is a tetrad in general relativity (GR)?

A tetrad, also known as a vierbein or frame field, is a set of four vector fields that span the tangent space of a curved spacetime in general relativity. It is used to define a local coordinate system at each point in the spacetime, allowing for the calculation of physical quantities such as energy, momentum, and spin.

2. How is a tetrad different from a coordinate basis?

A tetrad is a set of four vectors that are orthonormal, meaning they are all perpendicular to each other and have a magnitude of 1. This is in contrast to a coordinate basis, where the basis vectors are not necessarily perpendicular or normalized. A tetrad is used to calculate physical quantities in a curved spacetime, while a coordinate basis is used to define coordinates in a flat spacetime.

3. What is the purpose of using a tetrad in GR?

A tetrad is useful in GR because it allows for the calculation of physical quantities in a curved spacetime. In general relativity, the laws of physics are described using tensors, which are defined in terms of the metric tensor. By using a tetrad, which relates the metric tensor to a flat Minkowski metric, we can calculate physical quantities without having to work with the complicated curved metric directly.

4. Are there different types of tetrads in GR?

Yes, there are different types of tetrads in GR, depending on the specific application. Some common types include the orthonormal tetrad, the null tetrad, and the Newman-Penrose tetrad. Each type has its own set of properties and can be used to solve different problems in general relativity.

5. Where can I find a good reference for tetrads in GR?

There are many resources available for learning about tetrads in GR, including textbooks, online lectures, and research articles. Some recommended references include "General Relativity" by Robert M. Wald, "Gravitation" by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, and "A First Course in General Relativity" by Bernard F. Schutz. Additionally, many universities offer courses on general relativity that cover tetrads in detail.