Modifying EFE to Match Newton's Gravity Predictions

  • Context: Undergrad 
  • Thread starter Thread starter Herbascious J
  • Start date Start date
  • Tags Tags
    Gravity Match
Click For Summary

Discussion Overview

The discussion explores the possibility of modifying the Einstein Field Equations (EFE) to align with Newton's law of gravity, examining the differences in predictions between these two frameworks. Participants investigate the implications of geometrical aspects of General Relativity (GR) and the conditions under which Newtonian gravity can be seen as a limit of GR.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether the EFE can be modified to yield predictions identical to Newton's law of gravity, suggesting that while a geometric formulation exists (Newton-Cartan theory), it does not reduce to a modification of the EFE.
  • Others argue that Newtonian gravity lacks the concept of spacetime, which is fundamental to GR, indicating a fundamental difference in the frameworks.
  • One participant describes how GR contains Newtonian gravity as a low-speed, weak-field limit, where the metric tensor can be expressed as a perturbation of flat spacetime.
  • Another participant clarifies that the static condition in GR is crucial for the Newtonian limit, noting that changing fields, such as those involving multiple gravitating bodies, complicate the application of Newtonian approximations.
  • There is a discussion about the conditions under which the Newtonian approximation remains valid, particularly in relation to the solar system's dynamics and the detection of deviations from Newtonian predictions, such as the perihelion precession of Mercury.
  • Participants explore the implications of non-static systems and how they can still yield accurate predictions under certain conditions, questioning the thresholds at which Newtonian predictions fail compared to GR.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between Newtonian gravity and GR, with some asserting that Newtonian gravity can be approximated under certain conditions, while others emphasize the limitations and differences inherent in the two theories. The discussion remains unresolved regarding the precise conditions under which Newton's predictions diverge from those of GR.

Contextual Notes

Participants note that the discussion involves assumptions about the static nature of gravitational fields and the applicability of Newtonian approximations in dynamic systems. The limitations of the Newtonian model in accurately predicting certain phenomena, such as the perihelion precession of Mercury, are highlighted, but no consensus is reached on the characterization of these limitations.

  • #31
PAllen said:
I don't understand this. What does the invariant speed have to do with time derivatives? In the c infinite limit, under several schemes, you have Newtonian gravity. Does that mean time derivatives can't exist in Newtonian physics??

Note, the c infinite limit of the Lorentz transform is the Galilean transform. Does that prevent time derivatives from existing?
I meant coordinate time derivatives on the metric, sorry for the confusion. These are multiplied by a factor 1\c and so constitute factors which drop out after the c-->oo limit. Of course, this has nothing to do with the derivatives in the geodesic eqn. w.r.t. the affine parameter ;)
 
Physics news on Phys.org
  • #32
PeterDonis said:
The Einstein-Infeld-Hoffman equations aren't differential equations. They are the Newton force equation, ##G m_1 m_2 / r^2##, plus first-order post-Newtonian corrections, summed over all pairs of bodies. Since the post-Newtonian correction terms are all multiplied by ##1 / c^2##, they all vanish in the limit ##c \to \infty##, leaving just the Newtonian force.
How are they not differential equations? They relate positions and first and second derivatives thereof. For n bodies, they are a system of n complicated second order differential equations. The Newtonian case is the same, only the equations are much simpler and of course are explicitly solvable for n=2.
 
  • Like
Likes   Reactions: haushofer
  • #33
PAllen said:
How are they not differential equations?

You're right, I was only looking at the RHS of the Newtonian case.
 

Similar threads

  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 21 ·
Replies
21
Views
7K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 29 ·
Replies
29
Views
6K
  • · Replies 22 ·
Replies
22
Views
4K
  • · Replies 15 ·
Replies
15
Views
6K