Tetrad Definition and 23 Threads

This is a problem from the textbook Supergravity ( by Daniel Z. Freedman and Antoine Van Proeyen ). I am trying to learn general relativity from this book. I am attempting to do the later part of the Exercise 7.14 ( on page 148 ). Basically it asks us to explicitly show that the Levi-Civita...

Hello, the Homework Statement is quite long, since it includes a lot of equations so I will rather post the as images as to prevent mistypes. We need to find the integral where with $$ J_m =(\sqrt{2}(r−ia\cos⁡θ))^{−1} i(r^2+a^2)\sin⁡(θ)j, $$ $$ J_n = - \frac{a \Delta}{ 2 \Sigma} \sin(\theta...

I'm reading "Differentiable manifolds: A Theoretical Physics Approach" by Castillo and on page 170 of the book a calculation of the Ricci tensor coefficients for a metric is illustrated. In the book the starting point for this method is the equation given by: $$d\theta^i = \Gamma^i_{[jk]}...

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...

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...

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...

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...

how to find tetrad of this metric the tetrad given is this one I m a newly born in General Relativity please help me out how this tetrad is derived

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...

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} -...

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.

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!

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...

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...

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...

Where can i read about the solution of Einstein equations with spherical symmetry in tetrad formalism?

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...

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)...

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?

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

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...

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