# Exploring the Role of Torsion in General Relativity

• bchui
In summary, the torsion tensor is not considered in the standard formulation of general relativity because it is required to have a unique connection on a manifold that is torsion-free and metric compatible. However, some have explored the implications of including the torsion term, leading to the development of the Einstein-Cartan theory and its incorporation into supergravity and M-Theory. For further reading, see Hehl's 1976 article from Rev. Mod Phs and a more recent article from arXiv.
bchui
I ahve always wondered why only the curvature term $$R_{\mu,\nu}$$ been considered in GR. From differential Geoetry, how about the torsion tensor?

The simple answer is that in standard formulation of general relativity, we require a unique connection on a manifold which is torsion-free and metric compatible, which lead to the properties of the covariant derivative that we need.

It always bothered me as well that the torsion term was simply ignored. Many people have examined what happens when you keep the term, which has led to the Einstein-Cartan theory as a way to try and incorporate spin. Although this theory doesn't appear to be fundamental, it does seem to embed itself into supergravity which is in turn one of the limits of M-Theory.

Here is a link to Hehl's 1976 article from Rev. Mod Phs...
http://prola.aps.org/abstract/RMP/v48/i3/p393_1

And here is a much more recent article
http://arxiv.org/abs/0711.1535

## 1. What is torsion and how does it relate to general relativity?

Torsion is a mathematical concept that describes the twisting or rotation of a physical object. In general relativity, torsion is used to describe the curvature of spacetime caused by the presence of mass and energy.

## 2. How does torsion affect the behavior of objects in spacetime?

Torsion can cause objects to follow curved paths through spacetime, much like how gravity causes objects to follow curved paths in space. This is because torsion is related to the curvature of spacetime, which determines the paths that objects will take.

## 3. Can torsion explain phenomena such as dark energy and dark matter?

Some scientists have proposed theories that use torsion to explain the effects of dark energy and dark matter. However, there is currently no concrete evidence to support these theories and they remain speculative.

## 4. How is torsion measured and observed in experiments?

Torsion can be measured indirectly through its effects on the curvature of spacetime. This can be done through precise measurements of the motion of objects in space or by observing the bending of light around massive objects.

## 5. What implications does torsion have for our understanding of the universe?

Torsion plays a crucial role in our understanding of gravity and the behavior of objects in spacetime. It also has implications for theories beyond general relativity, such as string theory and loop quantum gravity, which incorporate torsion into their models of the universe.

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