Deriving the equations of motion in f(T) gravity

In summary, the conversation is about finding papers that explain the equations of motion in f(T) gravity. The person asking is specifically looking for a derivation for f(T) where the action is varied with respect to the vierbein. Another person suggests a link that provides some expository material on the topic. The original poster confirms that the link is helpful and thanks the person for their assistance.
  • #1
birdhen
35
0
Hi there,

I originally posted this in the SR, GR section so sorry for the re-post.

Can anyone point me in the direction of any papers that explicitly derive the equations of motion in f(T) gravity. I have seen the wikipedia derivation in f(R) gravity but can't find anything for f(T) where the action is varied wrt to the vierbein.

Many thanks
 
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  • #2
f(T) means teleparallel gravity ?

If so, http://www.ift.unesp.br/gcg/tele.pdf" seems to have some expository material including the Lagrangian and variational prinicple. I haven't read it myself, and it's not a field with which I'm familiar, but maybe it helps ...?
 
Last edited by a moderator:
  • #3
HI there,
Thank you for your reply, yes, f(T) gravity is an extension of teleparallel gravity.

PS I can't get your link to work, it just comes up blank.

Cheers
 
  • #4
Hi there,

I have moved to another computer and can open it fine now. Thanks very much it is very helpful!
 

Related to Deriving the equations of motion in f(T) gravity

1. What is f(T) gravity and how does it differ from traditional gravity theories?

f(T) gravity is a modified version of Einstein's theory of general relativity, where the gravitational field is described by a function of the torsion scalar T instead of the curvature scalar R. This means that f(T) gravity takes into account both curvature and torsion effects, whereas traditional theories only consider curvature. This leads to different equations of motion and potentially different predictions for the behavior of gravity on large scales.

2. How are the equations of motion derived in f(T) gravity?

The equations of motion in f(T) gravity are derived using the variational principle, which states that the true equations of motion are obtained by minimizing the action integral. In this case, the action integral is a function of the torsion scalar, and the field equations are obtained by varying this integral with respect to the metric tensor. This results in a set of second-order differential equations that describe the behavior of gravity in f(T) gravity.

3. What are the implications of f(T) gravity for cosmology?

f(T) gravity has been proposed as a possible alternative to traditional theories of gravity in explaining the accelerated expansion of the universe. It has been shown that f(T) gravity can reproduce the observed expansion without the need for dark energy or other exotic components. Additionally, f(T) gravity may also provide a solution to the cosmological constant problem, which is a major challenge in traditional theories of gravity.

4. Are there any observational tests for f(T) gravity?

There have been several proposed tests for f(T) gravity, including observations of the cosmic microwave background, gravitational lensing, and the dynamics of galaxies and clusters of galaxies. So far, these tests have not conclusively ruled out f(T) gravity as a viable theory, but more data and further analysis are needed to fully determine its validity.

5. How does f(T) gravity relate to other modified gravity theories?

f(T) gravity is just one of many proposed modifications to traditional theories of gravity, such as f(R) gravity and scalar-tensor theories. Each of these theories has its own unique features and implications, but they all share the goal of trying to explain the observed behavior of gravity on large scales. f(T) gravity, in particular, has gained significant attention in recent years due to its potential to address longstanding problems in traditional theories, but more research is needed to fully understand its implications and limitations.

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