Stress-energy tensor for a rotating object

[stevebd1]

I'm currently looking at stress-energy tensors and while I understand that T₀₀ is density and T₁₁, T₂₂ and T₃₃ are pressure, where does angular momentum fit in this? I'm assuming the quantities T₂₁, T₃₁ and T₃₂ might have something to do with this. For example, how would you incorporate the rotational kinetic energy of a neutron star with a frequency of 1000 Hz? $(E_k=1/2\cdot 0.4mr^2\cdot (f\pi2)^2)$ Also, when might the shear stress quantities, T₁₂, T₁₃ and T₂₃ apply? Cheers.

Steve

 

[Mentz114]

I think angular momentum is in the T_0k terms. This represents an energy flow, which clearly exists in a rotating object.

 

[Entropia]

,

The stress-energy tensor for a rotating object takes into account both mass-energy and angular momentum. The quantities T21, T31, and T32 represent the components of the tensor that correspond to the angular momentum of the object. This means that they describe the flow of angular momentum in different directions.

To incorporate the rotational kinetic energy of a neutron star with a frequency of 1000 Hz, you would need to calculate the energy density at each point in the object using the formula you provided (E_k=1/2\cdot 0.4mr^2\cdot (f\pi2)^2). This energy density would then be included in the T00 component of the tensor, which represents the total energy density of the object.

The shear stress quantities, T12, T13, and T23, would apply in situations where there is a shearing force acting on the object, such as in the case of a rotating object. These components of the tensor represent the stresses that arise due to the object's rotation and its resistance to deformation.

I hope this helps clarify the role of angular momentum and shear stress in the stress-energy tensor for a rotating object. Let me know if you have any further questions. Cheers!