Energy density in Stress Energy Tensor

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SUMMARY

The energy density in the stress-energy tensor is defined as the amount of energy stored in a system per unit mass, represented mathematically as T00. In a 4x4 matrix representation, the time dimension is commonly indexed as 0, which explains why T00 is used instead of T11. The concept of energy density can be further clarified as energy per unit volume, providing a clearer understanding of its mathematical implications.

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  • Understanding of the stress-energy tensor in general relativity
  • Familiarity with tensor notation and matrix representation
  • Basic knowledge of energy density concepts in physics
  • Mathematical proficiency in handling 4-dimensional space
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Physicists, students of general relativity, and anyone interested in understanding the mathematical foundations of energy density in the context of the stress-energy tensor.

shounakbhatta
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Hello,

I am new to this, if somebody could help me:

The energy density in stress-energy-tensor is the amount of energy stored in a given system per unit mass. The T00=energy density.

In a 4x4 matrix, we generally start with 1,1. Why it is 0,0?

Secondly, what does energy density mean mathematically? I am unable to get over the concept.

Thanks,

-- Shounak
 
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It's common (but not universal) to number the time dimension as 0 instead of 4 (x, y, and z or other spatial directions would be 1-3). It doesn't make a big difference either way.

Energy density = energy per unit volume.
 
Ok, thanks a lot.
 

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