Coupling torsion to electromagnetism and torsion tensor decomposition

  • #1
nicopa
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0
TL;DR Summary
Reason why the traceless part of the torsion tensor is usually set to zero in theories that extend general relativity to include electromagnetism?
When extending general relativity to include electromagnetism, several authors (e.g. Novello, Sabbata ecc.) assume that the traceless part of the torsion tensor vanishes or is deliberately set to zero. Then, either the trace or axial part of the torsion is used in association with the electromagnetic potential (coupling). Is there any reason why, besides mathematical convenience, the leftover part of the torsion is set to zero?
Is it related to gauge invariance?

Furthermore, is it correct to consider the decomposition of the torsion tensor into three components - i.e., trace part, axial part, and traceless part - as the most general one?
The decomposition I'm referring to is the following: $$T^λ_{μν} = \bar{T}^λ_{μν}+\frac{1}{6}ϵ_{λμνρ}V^ρ+\frac{1}{3}(g_{λν}T_μ − g_{λμ}T_ν)$$ where ##\bar{T}^λ_{μν}## is the traceless part of torsion, ##V^ρ## is the axial torsion vector or "pseudo-trace" and ##T_μ## is the torsion trace vector. This is found for example in Sur and Bhatia (Appendix, A-7 to A-10).
 
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  • #2
Is there anyone who can answer? Does the question need clarification?
 
  • #3
nicopa said:
several authors (e.g. Novello, Sabbata ecc.)
Do you have any specific references?
 
  • #4
nicopa said:
is it correct to consider the decomposition of the torsion tensor into three components - i.e., trace part, axial part, and traceless part - as the most general one?
What do you mean by "most general"?
 
  • #5
  • #6
PeterDonis said:
What do you mean by "most general"?
I mean that it doesn't require any assumptions as to a specific form of the torsion tensor, e.g. with vanishing traceless part. In other words, that the above mentioned decomposition of the torsion tensor doesn't imply any geometrical constraints on its components.
 

FAQ: Coupling torsion to electromagnetism and torsion tensor decomposition

What is the significance of coupling torsion to electromagnetism?

Coupling torsion to electromagnetism is significant because it extends the framework of classical field theory by incorporating geometric properties of spacetime. This can lead to new insights into the behavior of electromagnetic fields in the presence of torsional spacetime, potentially revealing new physical phenomena or providing a deeper understanding of existing ones.

How does torsion affect Maxwell's equations?

Torsion can modify Maxwell's equations by introducing additional terms that account for the torsional components of the spacetime. These modifications can alter the propagation of electromagnetic waves, leading to changes in their speed, polarization, and interaction with matter. The exact form of these modifications depends on the specific coupling model used.

What is the torsion tensor, and how is it decomposed?

The torsion tensor is a geometric object that represents the antisymmetric part of the connection in a spacetime with torsion. It can be decomposed into three irreducible components: the trace vector, the axial vector, and the purely tensorial part. This decomposition helps in analyzing the physical effects of torsion by isolating different contributions to the torsional field.

Can torsion provide an alternative explanation for dark matter or dark energy?

There are theoretical models suggesting that torsion could contribute to the effects attributed to dark matter or dark energy. For instance, torsional fields might influence the dynamics of galaxies or the expansion of the universe in ways that mimic the presence of dark matter or dark energy. However, these ideas are still speculative and require further investigation and empirical support.

What are the challenges in experimentally detecting torsion in spacetime?

Detecting torsion experimentally is challenging because its effects are typically very weak and can be easily overshadowed by other physical phenomena. Precise measurements of gravitational and electromagnetic fields, high-energy particle interactions, and cosmological observations are required to identify subtle signatures of torsion. Developing sensitive and accurate experimental techniques is crucial for advancing this area of research.

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