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Arcon
There is often talk of mass and energy in this forum. I tend to use the notion of relativistic mass myself since I believe it to be the most precise and consistent way of defining mass. However I also hold that the complete description of relativistic mass is a tensor of rank 2. I call it the mass tensor, M. MTW discuss something very similar to this in their text as well but they call it the inertial mass tenso. That mass must be a tensor is what Einstein meant when he wrote
Tuv = Muvc2
This too is discussed in MTW. They use the equality Energy = Mass, where "Mass" refers to "relativistic mass", to prove that Tuv is a symnetric tensor.
The page which describes the mass tensor is here
http://www.geocities.com/physics_world/sr/mass_tensor.htm
Arcon
The term energy-tensor, referring to Tuv, is not a necessary term. The same phenomena can be described in terms of a mass tensor. This follows from relativity due to the equivalence of mass and energy. The two differ only by the constant c2 but are defined differently. For instance, the T0k is energy flux in the kth direction while M0k is the kth component of momentum density. Due to the equivalence of mass and energyThe special theory of relativity has led to the conclusion that inert mass is nothing more or less than energy, which finds its complete mathematical expression in a symmetrical tensor of second rank, the energy-tensor.
Tuv = Muvc2
This too is discussed in MTW. They use the equality Energy = Mass, where "Mass" refers to "relativistic mass", to prove that Tuv is a symnetric tensor.
The page which describes the mass tensor is here
http://www.geocities.com/physics_world/sr/mass_tensor.htm
Arcon