Does Gravity Gravitate? Part 2 - Comments

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SUMMARY

The forum discussion centers on the nuances of mass definitions in General Relativity (GR) and their implications for understanding gravity. Key points include the distinction between the naive mass calculation (M_0) and the correct mass (M) derived from the energy-momentum tensor, as articulated in the Schwarzschild metric. Participants clarify that gravity cannot be switched off, and the concept of gravitational self-energy is critical in understanding why gravity does not gravitate. The discussion emphasizes the importance of correcting assumptions about Euclidean space when analyzing gravitational effects.

PREREQUISITES
  • Understanding of General Relativity (GR) principles
  • Familiarity with the Schwarzschild metric
  • Knowledge of the energy-momentum tensor and its trace
  • Basic concepts of Newtonian gravity and gravitational self-energy
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  • Explore the implications of the energy-momentum tensor in GR
  • Study the differences between M_0 and M in the context of gravitational calculations
  • Investigate the concept of gravitational self-energy in both Newtonian and relativistic frameworks
  • Learn about the ADM mass and its significance in General Relativity
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Physicists, students of theoretical physics, and anyone interested in the complexities of gravitational theory and its mathematical foundations.

  • #31
This is the Hilbert action, and it's unique (up to a cosmological constant, which is not included here) in being generally covariant and leading to 2nd-order equations of motion. This is so, because ##R## is the only scalar you can build from the pseudometric tensor that is only linear in the 2nd derivative with coefficients containing no derivatives, which means that via partial integration you can show that the action is a functional of a Lagrangian that only depends on the ##g_{\mu \nu}## and its first derivatives.
 
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