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dsaun777
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The stress energy tensor has many forms based on the type of matter you are describing, dust, fluid, perfect fluid... is it true that the trace of all of these matter situations is invariant?
The trace of any tensor is invariant under coordinate transformations.dsaun777 said:The stress energy tensor has many forms based on the type of matter you are describing, dust, fluid, perfect fluid... is it true that the trace of all of these matter situations is invariant?
dsaun777 said:is it true that the trace of all of these matter situations is invariant?
Dust is a particular case of a perfect fluid with ##w=0##. A perfect fluid has the trace ##\rho(1+3w)## of the stress-energy tensor, which can a priori take any value unless one starts introducing additional requirements on the equation of state parameter ##w##.PeterDonis said:And the trace of the stress-energy tensor describing a perfect fluid is also nonzero, but different from that of dust.
And w being pressure/ density?Orodruin said:Dust is a particular case of a perfect fluid with ##w=0##. A perfect fluid has the trace ##\rho(1+3w)## of the stress-energy tensor, which can a priori take any value unless one starts introducing additional requirements on the equation of state parameter ##w##.
Yes, in the rest frame of the fluid.dsaun777 said:And w being pressure/ density?
Orodruin said:Dust is a particular case of a perfect fluid with ##w=0##.
The stress energy tensor is a mathematical object used in the field of physics to describe the distribution of energy and momentum in a given space. It is a rank-2 tensor that relates the energy and momentum of a system to its curvature and gravitational field.
The stress energy tensor is important because it is a fundamental concept in general relativity and is used to describe the behavior of matter and energy in the universe. It is also a key component in Einstein's field equations, which describe the relationship between matter and the curvature of spacetime.
The stress energy tensor is calculated using the Einstein field equations, which involve the curvature of spacetime and the energy-momentum tensor. The energy-momentum tensor is calculated by summing the contributions of all the particles and fields in a given space.
The stress energy tensor has a physical interpretation as it represents the flow of energy and momentum in a given space. It also describes the distribution of matter and energy in the universe and how it affects the curvature of spacetime.
The stress energy tensor has various applications in the field of physics, including in cosmology, astrophysics, and high-energy physics. It is used to study the behavior of matter and energy in the universe, the formation of galaxies, and the dynamics of black holes and other astronomical objects.