The trace of the stress-energy tensor varies based on the type of matter described, such as dust, fluid, or perfect fluid. While the trace of any tensor is invariant under coordinate transformations, the specific values of the traces differ among these types. For instance, the trace for electromagnetic radiation is zero, while dust and perfect fluids have nonzero traces, with the latter being defined as ##\rho(1+3w)##, where ##w## represents the equation of state parameter. Dust is a specific case of a perfect fluid with ##w=0##.
PREREQUISITESPhysicists, particularly those specializing in general relativity, cosmology, and fluid dynamics, as well as students seeking to deepen their understanding of stress-energy tensors and their applications in theoretical physics.
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##.