# What is Tetrad: Definition and 22 Discussions

The tetrad is the four spores produced after meiosis of a yeast or other Ascomycota, Chlamydomonas or other alga, or a plant. After parent haploids mate, they produce diploids. Under appropriate environmental conditions, diploids sporulate and undergo meiosis. The meiotic products, spores, remain packaged in the parental cell body to produce the tetrad.

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3. ### I The spacetime length of finite spacelike intervals

Hello, I'm aware of the following topic has already been discussed here on PF, nevertheless I would like to go deep into the concept of "finite spacelike interval" in the context of SR and GR. All us know the physical meaning of timelike paths: basically they are paths followed through...
4. ### Exercise 16, chapter 3 (Tetrad) in Carroll

My attempt at solution: in tetrad formalism: $$ds^2=e^1e^1+e^2e^2+e^3e^3≡e^ae^a$$ so we can read vielbeins as following: \begin{align} e^1 &=d \psi;\\ e^2 &= \sin \psi \, d\theta;\\ e^3 &= \sin⁡ \psi \,\sin⁡ \theta \, d\phi \end{align} componets of spin connection could be written by using...
5. ### A Understanding Differential Forms: Torsion, Spin & Tetrad

I recently came across a paper (referenced below) containing the statement that:"The differential form notation is much more concise and elegant than the tensor notation, but both contain the same information.", and the paper left me with a desire to understand the notation of differential...
6. ### A Moller Tetrad Gravitational Lagrangian: Limits on Lambda?

This is a quite specific question, but maybe someone knows (part of) the answers, what would be much appreciated. The Moller (the o is a specific Danish character) Lagrangian for gravitation reads (see for example Aldrovandi-Pereira, Teleparallel Gravity, Springer 2013) ##L = \partial_\mu...

8. ### A Understanding the Tetrad Formalism in General Relativity

Correct me if I'm wrong. But my understanding is the following. Introducing a tetrad, means introducing an orthonormal basis of smooth vector fields, satisfying ##(e_{\mu})^{a}(e_{\nu})_{a} = \eta_{\mu\nu}## at each point. That is, we define a set of 4 vector fields such that they are...
9. ### A Strange Tetrad Form of Einstein-Hilbert Action

I have seen it the claimed that the Einstein-Hilbert action can be written in terms of a tetrad ##e_{\mu} \, ^a## as \begin{align} S &= \int d^n x \, e R(e_{\mu} \, ^a, \omega_{\mu a} \, ^b (e)) \\ &= \int d^n x \, e (T_{ca} \, ^a T^{cb} \, _{b} - \frac{1}{2} T_{ab \ c} T^{ac \ b} -...
10. ### I Tetrad formalism outside of the equatorial plane

I'm interesting in about possibility to express a tetrad of a rotating matter in neutron star (in some approximate known metric, where shape of star is unchanged - Lense-Thirring metric) outside of the equatorial plane. My idea is: I start from Locally Non Rotating Frame (LNRF) in equatorial...

Bill_K submitted a new PF Insights post Tetrad Fields and Spacetime Continue reading the Original PF Insights Post.
12. ### Affine Connection Γ in Terms of Tetrad: Help Needed

Hi, some one know the expression of the affine connection Γ in terms of tetrad formalism? I would like also some references if it's possible, i found a hit but i think that is wrong... please help me it's so important!
13. ### Series expansion tetrad Fermi coordinates

Hi all. I'm working on a project that requires me to perform calculations in Fermi normal coordinates to certain orders, mostly 2nd order in the distance along the central worldline orthogonal space-like geodesics. In particular I need a rotating tetrad propagated along the central worldline...
14. ### Tetrad Formalism: Finding e^{a \mu}?

I am new to tetrad formalism in general relativity. I understand that e^{a}_{\mu} is the component of a tetrad basis but what is meaning of e^{a \mu} and how do i find it? For example, e^{a}_{\mu} is a diagonal matrix (a,b,c,d), how do I find e^{a \mu}? Just raise the index using metric tensor...
15. ### Find tetrad component from metric

How can find components of tetrads from metric ? i know the relation between tetrads and metric g_{μ \nu}=η_{ab}e^{a}_{μ}e^{b}_{\nu} where e^{b}_{\nu} are component of tetrads , in the case of Schwarzschild that metric is diagonal , it is a easy problem but what about non-diagonal metric like...

17. ### How to obtain the transformation of Null Tetrad ?

Currently, I meet with the so-called null rotation in my study. I cannot understand why it has a mathematical form like that? Is there anyone familiar with this? Can anyone give a lucid explanation of it or provide steps to derive it. See the image above on the null transformation (in...
18. ### I am a bit confused at orthonormal tetrad in General Relativity

I am a bit confused at "orthonormal tetrad" in General Relativity... I think orthonormal tetrad should be a set of vectors like e0= (1,0,0,0) e1= (0,1,0,0) e2= (0,0,1,0) e3= (0,0,0,1) However, in my book, it is written as e0= (-1,0,0,0) e1= (0,1,0,0) e2= (0,0,1,0) e3= (0,0,0,1)...
19. ### How to denote tetrad in Abstract Index Notation ?

I like Penrose's Abstract Index Notation very much. I am familiar with using Abstract Index Notation to denote Coordinate Basis. But when I try to denote tetrad with Abstract Index Notation, I meet problems. How to denote tetrad in Abstract Index Notation?
20. ### Is there any good reference of tetrad in GR

I want to find a good reference in GR about the application of tetrad. Is there any good suggestions?
21. ### Why Use the Tetrad Formalism in General Relativity?

Could someone please explain briefly the advantange of doing GR in terms of the tetrad field instead of the metric? A little background for the beginners who may be reading. As originally formulated by Einstein the dynamical quantify of GR is the spacetime metric g_{\mu\nu}(x). One can...
22. ### Metric versus Tetrad formulation of relativity

Any opinions on the usage of tetrad instead of metric formulations of relativity?