I Energy Tensor Gradients: ∂βTμυ

  • I
  • Thread starter Thread starter dsaun777
  • Start date Start date
  • Tags Tags
    Energy Tensor
dsaun777
Messages
296
Reaction score
39
I understand, kind of, that ∇μTμυ=0 by conservation or coninuity. What would be ∂βTμυ when β=1,2,3 no time derivative.
 
Physics news on Phys.org
dsaun777 said:
I understand, kind of, that ∇μTμυ=0 by conservation or coninuity. What would be ∂βTμυ when β=1,2,3 no time derivative.
I hope that you are aware that there is a summation over ##\mu## in the first equation. What do you mean by "what would be..."? It is exactly what you have written, the partial derivative of a function, which is the component of a tensor in some coordinates.
 
martinbn said:
I hope that you are aware that there is a summation over ##\mu## in the first equation. What do you mean by "what would be..."? It is exactly what you have written, the partial derivative of a function, which is the component of a tensor in some coordinates.
I meant what would be the spatial gradient of the energy momentum tensor?
 
There's no general answer to this question...##\partial_\beta T_{\mu\nu}## depends on the stress energy tensor and the coordinates you chose...it's like asking "what's ##d\vec{v}/dt##?" without specifying anything about ##\vec{v}##. It's hard to figure out what you're trying to get at.

At most, I can say, in 4-D spacetime, with the restriction that ##\beta=1,2,3##, then ##\partial_\beta T_{\mu\nu}## is a set of 48 numbers.
 
Matterwave said:
There's no general answer to this question...##\partial_\beta T_{\mu\nu}## depends on the stress energy tensor and the coordinates you chose...it's like asking "what's ##d\vec{v}/dt##?" without specifying anything about ##\vec{v}##. It's hard to figure out what you're trying to get at.

At most, I can say, in 4-D spacetime, with the restriction that ##\beta=1,2,3##, then ##\partial_\beta T_{\mu\nu}## is a set of 48 numbers.
For some incompressable fluid with density ρ(xμ,t ) at rest what is gradient of the stress energy tensor Tαβ
 
dsaun777 said:
I understand, kind of, that ∇μTμυ=0 by conservation or coninuity. What would be ∂βTμυ when β=1,2,3 no time derivative.
T_{\mu\nu:\beta} is covariant component of a three rank tensor allowing $$\beta=0,1,2,3$$ though I do not know if there is a physical meaning on it.
 
I asked a question here, probably over 15 years ago on entanglement and I appreciated the thoughtful answers I received back then. The intervening years haven't made me any more knowledgeable in physics, so forgive my naïveté ! If a have a piece of paper in an area of high gravity, lets say near a black hole, and I draw a triangle on this paper and 'measure' the angles of the triangle, will they add to 180 degrees? How about if I'm looking at this paper outside of the (reasonable)...
Thread 'Relativity of simultaneity in actuality'
I’m attaching two figures from the book, Basic concepts in relativity and QT, by Resnick and Halliday. They are describing the relativity of simultaneity from a theoretical pov, which I understand. Basically, the lightning strikes at AA’ and BB’ can be deemed simultaneous either in frame S, in which case they will not be simultaneous in frame S’, and vice versa. Only in one of the frames are the two events simultaneous, but not in both, and this claim of simultaneity can be done by either of...
Back
Top