The spacetime curvature changed by an object

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SUMMARY

The discussion centers on the relationship between spacetime curvature and mass, specifically addressing whether the curvature is influenced by relativistic mass or rest mass. It concludes that the modern consensus is to avoid the concept of relativistic mass, advocating instead for the use of invariant mass and the formula for momentum as γmv. The stress-energy tensor is identified as the source term for gravity in general relativity, emphasizing the importance of clarity in terminology to prevent confusion.

PREREQUISITES
  • Understanding of general relativity and the stress-energy tensor
  • Familiarity with the concepts of invariant mass and relativistic effects
  • Knowledge of the Lorentz factor (γ) and its application in physics
  • Basic grasp of momentum in classical and relativistic contexts
NEXT STEPS
  • Research the implications of the stress-energy tensor in general relativity
  • Study the differences between invariant mass and relativistic mass
  • Explore the concept of momentum in relativistic physics, focusing on γmv
  • Examine the historical context and evolution of mass terminology in physics
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Physicists, students of general relativity, and anyone interested in the nuances of mass and momentum in the context of spacetime and gravity.

KallaNikhil
Does the amount by which an object changes the spacetime curvature depend on relativistic mass or the rest mass? Through this question I just want to answer whether momentum equals [relativistic mass * velocity] or is it [rest mass * gamma * velocity]. Both the formulas might be the same but I think they are different conceptually
 
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The source term for gravity in general relativity is the stress-energy tensor.

The modern (last thirty+ years, although pop-sci hasn't caught on yet) recommendation is to forget relativistic mass. It just tends to cause confusion - such as people guessing that it's the source of gravity. It's not. Stick with mass, meaning invariant mass, and use ##\gamma m## where needed.
 
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KallaNikhil said:
Both the formulas might be the same but I think they are different conceptually

It's better to think of the momentum as ##\gamma mv## rather than calling ##\gamma m## the relativistic mass. But that's just a matter of preference.
 

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