Calculate metric tensor in terms of Mass

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SUMMARY

The discussion focuses on calculating the metric tensor in General Relativity (GR) in relation to mass when objects are moving slowly. The relevant equation provided is R00 - ½g00R = 8πGT00 = 8πGmc², which links the Ricci tensor and the energy-momentum tensor to mass. Participants are encouraged to reference the slow-motion weak-field limit of GR and the Schwarzschild solution to understand the relationship between mass and the Schwarzschild radius.

PREREQUISITES
  • General Relativity (GR) fundamentals
  • Understanding of the Ricci tensor and energy-momentum tensor
  • Knowledge of the Schwarzschild solution
  • Familiarity with the concept of the Schwarzschild radius
NEXT STEPS
  • Study the slow-motion weak-field limit of General Relativity
  • Research the Schwarzschild solution in detail
  • Explore the derivation of the Schwarzschild radius
  • Learn about the implications of mass-energy equivalence in GR
USEFUL FOR

This discussion is beneficial for students and researchers in physics, particularly those focusing on General Relativity, theoretical physicists, and anyone interested in the mathematical foundations of gravitational theories.

Gajanand Jha
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Homework Statement


Suppose everything is moving slowly, How can we find the metric tensor in GR in terms of the mass contained.

Homework Equations


I understand in case of everything moving slowly only below equation is relevant -

R00 - ½g00R = 8πGT00 = 8πGmc2

The Attempt at a Solution


None.
 
If you still have not solved this...

Look in your text for the slow-motion weak-field limit of GR. Alternatively, look for the Schwarzschild solution and how the mass of the central object is related through this solution to the Schwarzschild radius.
 

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