Undergrad Cartan's Understanding of Einstein Field Equation

Click For Summary
Cartan's geometric interpretation of the Einstein Field Equation suggests that the equation relates the sum of moments of rotation within a 3-cube to the energy-momentum contained in that space. This interpretation is primarily discussed in John Wheeler's works, particularly in "Gravitation" (MTW), while other popular texts like Wald do not cover it. Wheeler is credited with bringing Cartan's ideas to broader attention, highlighting the significance of his coordinate-free differential geometry. The lack of adoption of Cartan's viewpoint may stem from its complexity and the sophistication required to understand it. Overall, Cartan's insights offer a unique perspective on the relationship between geometry and physics in the context of general relativity.
dx
Homework Helper
Messages
2,143
Reaction score
52
TL;DR
Cartan and general relativity
About a week ago I was reading about Cartan's geometric interpretation of the Einstein Field Equation

Gij + Λgij = κTij

According to Cartan, this equation expresses the idea

(sum of moments of rotation for the faces of a little 3-cube) = 8π * (amount of energy-momentum within that 3-cube)

As far as I can tell, it is only in John Wheeler's various books (MTW, but also his other books) where this idea of Cartan is explained. None of the other popular books like Wald discuss this. Apparently, it was Wheeler who dug it out of Cartan's papers and made it widely known. If anyone on this forum has a good understanding of this, I would appreciate it if you can share/explain this. Also, why don't more people and books adopt this viewpoint? Is it because Cartan's coordinate free differential geometry is too sophisticated?
 
Last edited by a moderator:
Physics news on Phys.org
Frankly I don't know why...Btw MTW has also a section for the Cartan's geometric interpretation of Newton spacetime (basically the Poisson equation).
 

Thread 'Am I understanding the concept of proper frame of reference?'

MOVING CLOCKS In this section, we show that clocks moving at high speeds run slowly. We construct a clock, called a light clock, using a stick of proper lenght ##L_0##, and two mirrors. The two mirrors face each other, and a pulse of light bounces back and forth betweem them. Each time the light pulse strikes one of the mirrors, say the lower mirror, the clock is said to tick. Between successive ticks the light pulse travels a distance ##2L_0## in the proper reference of frame of the clock...
View full post »

Similar threads

Einstein-Cartan Field Equations Derivation
  • · Replies 2 ·
Replies
2
Views
2K
Fermionic Fields in Einstein Field Equations | Explained
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Einstein and Spacetime: Debunking the Myth of Rejecting Curvature
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad How Do Physical Quantities Relate to Spacetime in Einstein's Field Equations?
  • · Replies 8 ·
Replies
8
Views
2K
Deriving Field Equations of Einstein-Cartan Theory from Hilbert Action
  • · Replies 8 ·
Replies
8
Views
9K
Understanding Einstein Field Equation & Metric Tensor
  • · Replies 10 ·
Replies
10
Views
3K
Derivations of Einstein field equations
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Benefits & Disadvantages of Palatini Action for General Relativity
  • · Replies 2 ·
Replies
2
Views
2K
Understanding Einstein's field equations
  • · Replies 5 ·
Replies
5
Views
2K
Understanding Einstein's Field Equations Solutions
  • · Replies 1 ·
Replies
1
Views
2K