Shear stress energy tensor in GR

In summary, there is a stress-energy-momentum tensor in General Relativity that includes both shear and non-shear stress. This tensor is a conserved quantity and can define pressure, but pure shear stress tensors may not necessarily be conserved. Lorentz transformations can also transform non-shear stress into shear stress, causing paradoxes such as the lever paradox.
  • #1
blue_sky
53
0
Where can I found an expressionfor the shear stress tensor in GR with some explanation about it?

Thanks

blue
 
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  • #2
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
 
  • #3
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.
 
  • #4
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
 
  • #5
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
 

What is the shear stress energy tensor in general relativity?

The shear stress energy tensor in general relativity is a mathematical object used to describe the distribution of energy and momentum in spacetime. It is a 4x4 matrix that contains information about the stress and shear forces present in a given region of spacetime.

How is the shear stress energy tensor related to Einstein's field equations?

The shear stress energy tensor is one of the terms in Einstein's field equations, which describe the curvature of spacetime in the presence of matter and energy. It represents the contribution of matter and energy to the overall curvature of spacetime.

What is the physical significance of the shear stress energy tensor?

The shear stress energy tensor is important in understanding the dynamics of matter and energy in the universe. It allows us to calculate the effects of gravity on matter and energy, and to make predictions about the behavior of objects in spacetime.

How is the shear stress energy tensor calculated?

The shear stress energy tensor is calculated using the stress-energy-momentum tensor, which takes into account not only the distribution of matter and energy, but also the flow of energy and momentum. It is a complex mathematical process that involves integrating the contributions of all matter and energy in a given region of spacetime.

What are some real-world applications of the shear stress energy tensor?

The shear stress energy tensor has many practical applications in the field of astrophysics and cosmology. It is used to study the behavior of matter and energy in extreme environments, such as black holes and neutron stars. It also helps us to understand the expansion of the universe and the formation of large-scale structures, such as galaxies and galaxy clusters.

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