Stress Energy Tensor vs Energy Momentum Tensor

In summary, the Stress Energy Tensor and Energy Momentum Tensor are both mathematical representations of energy and momentum distribution in a physical system. While the Stress Energy Tensor is used in General Relativity, the Energy Momentum Tensor is used in Special Relativity. The mathematical equation for the Stress Energy Tensor is T<sub>μν</sub> = (ρ + p)u<sub>μ</sub>u<sub>ν</sub> - pg<sub>μν</sub>, and it is used in Einstein's field equations to describe the curvature of spacetime. The two tensors represent energy, momentum, stresses, and pressure, with the Stress Energy Tensor being a more comprehensive version. In the absence of gravity, the two tensors are
  • #1
captain
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is the stress energy tensor the same as the energy momentum tensor?
 
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  • #2
captain said:
is the stress energy tensor the same as the energy momentum tensor?
The stress tensor is part of the stress-energy-momentum tensor, T^uv (u,v = 1,2,3). The stress tensor s^jk (j,k = 1,2,3) is given by s^jk = T^jk.

Pete
 
  • #3


The terms stress energy tensor and energy momentum tensor are often used interchangeably, but they do have slightly different meanings. The stress energy tensor is a mathematical object that describes the distribution of energy and momentum in a physical system, while the energy momentum tensor is a more general term that can describe the distribution of any conserved quantity in a system.

In the context of general relativity, the stress energy tensor is used to describe the distribution of energy and momentum in the gravitational field, while the energy momentum tensor is used to describe the distribution of all conserved quantities, including energy, momentum, and angular momentum. Therefore, while the stress energy tensor is a subset of the energy momentum tensor, they are not exactly the same.

In summary, while the stress energy tensor and energy momentum tensor are closely related and often used interchangeably, they have slightly different meanings and contexts in physics.
 

What is the difference between Stress Energy Tensor and Energy Momentum Tensor?

The Stress Energy Tensor and Energy Momentum Tensor are both mathematical representations of the distribution of energy and momentum in a physical system. However, the Stress Energy Tensor is used in the context of General Relativity, while the Energy Momentum Tensor is used in the context of Special Relativity.

What is the mathematical equation for the Stress Energy Tensor?

The mathematical equation for the Stress Energy Tensor is Tμν = (ρ + p)uμuν - pgμν, where ρ is the energy density, p is the pressure, uμ is the four-velocity, and gμν is the metric tensor.

How is the Energy Momentum Tensor used in Einstein's field equations?

The Energy Momentum Tensor is used in Einstein's field equations as a source for the curvature of spacetime. It describes the distribution of energy and momentum, which in turn affects the curvature of spacetime according to the principles of General Relativity.

What physical quantities are represented by the Stress Energy Tensor and Energy Momentum Tensor?

The Stress Energy Tensor represents energy, momentum, and stresses in a gravitational field, while the Energy Momentum Tensor represents energy and momentum in a flat, non-gravitational context. Both tensors also include the effects of pressure.

How are the Stress Energy Tensor and Energy Momentum Tensor related?

The Stress Energy Tensor is a more general and comprehensive version of the Energy Momentum Tensor. In the absence of gravity, the two tensors are equivalent. However, in the presence of gravity, the Stress Energy Tensor accounts for the additional effects of spacetime curvature.

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