Calculating Stress Energy Tensor for Rotating Bodies

In summary, the stress energy tensor is a mathematical tool used to describe the distribution of energy and momentum in a rotating body. It takes into account both the rotational and translational motion of the body, as well as the effects of gravity and other external forces. By calculating the stress energy tensor, scientists can better understand the physical properties and behavior of rotating bodies, such as planets and stars. This information is crucial for studying celestial objects and predicting their movements and interactions with other bodies in the universe.
  • #1
fobos3
34
1
Hello, can someone explain to me how to calculate the stress energy tensor. If we remove the first row and column, we get get the stress tensor, which I am not familiar with, or am I missing something here? But what about the components of the first column and row. What I know so far is that [tex]T^{ab}=\texttt{pressure for $ (a,b) \in (1,3)$}[/tex]. Everything else is pitch black. I am interested in the stress-energy tensor of a rotating body.
Any feedback will be appreciated.
 
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  • #2
The http://en.wikipedia.org/wiki/Stress-energy_tensor" has a figure that describes each component of the tensor.
 
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  • #3
Rotating Stars in Relativity
Nikolaos Stergioulas
http://relativity.livingreviews.org/Articles/lrr-2003-3/

Maybe Eq 11 or thereabouts.
 
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FAQ: Calculating Stress Energy Tensor for Rotating Bodies

1. What is the stress energy tensor and why is it important in calculating stress for rotating bodies?

The stress energy tensor is a mathematical object used to describe the distribution of stress, momentum, and energy in a given system. In the context of rotating bodies, it is important because it allows us to quantify the effects of rotation on these physical quantities.

2. How is the stress energy tensor calculated for rotating bodies?

The stress energy tensor for rotating bodies can be calculated using equations derived from Einstein's field equations in general relativity. This involves taking into account the rotational motion of the body and its effects on spacetime curvature.

3. What factors influence the stress energy tensor for rotating bodies?

The stress energy tensor for rotating bodies is influenced by several factors, including the mass and angular momentum of the body, the speed of rotation, and the distribution of matter within the body. Additionally, the stress energy tensor can be affected by external forces acting on the body.

4. How is the stress energy tensor used in studying the behavior of rotating bodies?

The stress energy tensor is used in various fields of study, such as astrophysics and cosmology, to understand the behavior of rotating bodies. It allows scientists to predict the effects of rotation on the structure and dynamics of these bodies, as well as to make predictions about their eventual fate.

5. Are there any limitations or assumptions in using the stress energy tensor for rotating bodies?

Like any mathematical model, the stress energy tensor for rotating bodies has limitations and assumptions. For example, it assumes that the body is rotating in a vacuum and that the effects of rotation can be described within the framework of general relativity. Additionally, it may not fully capture the behavior of highly complex or extreme rotating bodies.

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