On modified theories of gravity

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SUMMARY

The discussion centers on modified theories of gravity and their relationship to the Schwarzschild solution in General Relativity (GR). It is established that any modified theory must replicate the Schwarzschild solution to remain valid under solar-system experiments, which include light deflection and the perihelion shift of Mercury. The consensus is that while modified theories can deviate in strong fields or galactic scales, they must align with Newtonian gravity and GR's first-order predictions in weak fields. The book "Was Einstein Right?" is recommended for further exploration of this topic.

PREREQUISITES
  • Understanding of General Relativity (GR)
  • Familiarity with the Schwarzschild solution
  • Knowledge of Newtonian gravity principles
  • Basic concepts of weak and strong gravitational fields
NEXT STEPS
  • Research the implications of the Schwarzschild solution in modified theories of gravity
  • Explore the book "Was Einstein Right?" for deeper insights
  • Investigate the differences between weak and strong field predictions in gravity theories
  • Examine experimental tests of gravity theories in solar-system contexts
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Physicists, astrophysicists, and students interested in gravitational theories and their implications on cosmological observations.

xiaomaclever
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I am confused about the modified theories of gravity. We all know there is the Schwarzschild solution for GR. The solution can give right prediction for the solar-system experiments, such as Light deflection, perihelion shift of the Mercury and gravitational time delay. Whether all kinds of modified theories of gravity should have the same Schwarzschild solution, otherwise they will be ruled out by the solar-system experiments. I know some modified theories of gravity don't have the Schwarzschild-like solution for spherically symmetric vacuum spacetime.
 
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They all have to give Newtonian gravity and at least the same first order deviation as GR in weak fields (gravitation in the solar system is weak). They might give different results on a galactic scale (very weak fields) and in strong fields.
 
A good book on this topic is "Was Einstein Right?"
 

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