Shear stress energy tensor in GR

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Discussion Overview

The discussion revolves around the concept of the shear stress tensor in the context of General Relativity (GR), specifically seeking expressions and explanations related to it. Participants explore the relationship between shear stress and the stress-energy tensor, as well as implications of shear stress in relativistic frameworks.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests an expression for the shear stress tensor in GR, indicating a need for clarification on the topic.
  • Another participant expresses unfamiliarity with the term "shear stress tensor," suggesting that the stress-energy-momentum tensor may be what is being referred to.
  • It is proposed that pressure in the stress-energy tensor could encompass shear stress contributions, highlighting the tensor's conserved nature.
  • A participant recalls that the stress-energy tensor includes both shear and non-shear stress, and mentions that Lorentz transformations can convert non-shear stress into shear stress, leading to potential paradoxes.
  • The initial requester confirms that they are indeed referring to shear stress in the context of non-perfect fluids.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence or definition of a shear stress tensor in GR, with multiple competing views presented regarding its relationship to the stress-energy tensor.

Contextual Notes

There are unresolved assumptions regarding the definitions and implications of shear stress in GR, as well as the specific contexts in which these tensors are applied.

blue_sky
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Where can I found an expressionfor the shear stress tensor in GR with some explanation about it?

Thanks

blue
 
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blue_sky said:
Where can I found an expressionfor the shear stress tensor in GR with some explanation about it?

Thanks

blue
Sorry but I've never heard about such a thing. There's a stress-energy-momentum tensor. Is that what you're referring to?

Pete
 
Yes, I think you could define pressure in the stress-energy tensor to contain shear stress contributions. This tensor is a conserved quantity, which a pure shear stress tensor in relativity would not necessarily be.
 
As I recall, the stress energy tensor will include both shear and non-shear stress. Furthermore, I'm pretty sure Lorentz transformations can transform non-shear stress into shear stress. This causes some interesting paradoxes to arise, such as the lever paradox pointed out by genxhis in

this thread
 
pmb_phy said:
Sorry but I've never heard about such a thing. There's a stress-energy-momentum tensor. Is that what you're referring to?

Pete

Yes, for not perfect fluid.

blue
 

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