What is the Superpotential Tensor in Teleparallel Gravity?

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SUMMARY

The superpotential tensor in teleparallel gravity is defined as a mathematical construct whose divergence yields a conserved current, as established by the Bianchi identities. This divergence is inherently zero, indicating a fundamental property of the superpotential. For further insights, refer to "Gravity and Strings" by Ortin, specifically section 2.2, which elaborates on the implications of this tensor in the context of General Relativity (GR) and its relation to the conservation of the energy-momentum tensor.

PREREQUISITES
  • Understanding of teleparallel gravity concepts
  • Familiarity with Bianchi identities in differential geometry
  • Knowledge of energy-momentum tensor in General Relativity
  • Basic comprehension of superpotential definitions in theoretical physics
NEXT STEPS
  • Study the Bianchi identities and their implications in theoretical physics
  • Read "Gravity and Strings" by Ortin, focusing on section 2.2
  • Explore the role of superpotential tensors in various gravitational theories
  • Investigate the relationship between general covariance and conservation laws in GR
USEFUL FOR

The discussion is beneficial for theoretical physicists, researchers in gravitational theories, and students studying advanced concepts in General Relativity and teleparallel gravity.

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what is the meaning of superpotential tensor in teleparallel gravity ? it defined as :


2nuirt3.png
 
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Looking at

http://cds.cern.ch/record/478192/files/0011079.pdf

it seems that the divergence of this superpotential yields the conserved current due to the Bianchi identities. The divergence of this superpotential is then automatically zero.

You should check "Gravity and Strings" by Ortin, section 2.2 for some extra comments on this superpotential :)

So in the context of GR I would say that gct-invariance implies conservation of the energy momentum tensor, and this energy momentum tensor can be written as the divergence of the superpotential due to the Bianchi identities.
 
Thank u dude
 

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