Understanding Einstein-Hilbert Action: Detailed Explanation from an Expert

In summary, the appropriate action is used to derive the field equations by setting variations of it with respect to the metric equal to zero. This action is chosen because it is the simplest, most general scalar that encodes the curvature of spacetime. It involves the inverse metric, the Ricci tensor, and other components, making it a comprehensive and informative choice for the field equations. This principle, known as variational mechanics, may seem exotic to those encountering it for the first time, but it is a fascinating and important topic to gain insight into.
  • #1
Terilien
140
0
Can someone explain to me why this is the appropriate action?It makes some sens that that would be used, but I'd like a detailed explanation from someone familiar with the topic.

Why is it the one that yields the proper equations?
 
Last edited:
Physics news on Phys.org
  • #2
Well, for a start, you can derive the field equations by setting variations of this action with respect to the metric equal to zero. This is done in many GR texts.
 
  • #3
Yes but what is the intuition behind it? What lead hilbert to choose that particular action?
 
  • #4
Can you think of a simpler scalar that encodes the curvature of spacetime? The Ricci scalar is a fairly obvious choice.
 
  • #5
So essentially it used because its the simplest, most general(encodes curvature) involves the inverse metric, the ricci tensor, etc.. and such. So essentially its simple and encodes all the information that we may want tin the field equations...


This is the first time I've emcountered this topic(variational mechanics) so it seems quite exotic. Its very interesting though.

It would however be nice, to gain whatever insight I can into this principle and this topic in general.
 
Last edited:

1. What is the Einstein-Hilbert Action?

The Einstein-Hilbert Action is a mathematical formulation of Einstein's Theory of General Relativity. It is used to describe the behavior of gravity in terms of the curvature of space and time.

2. Why is the Einstein-Hilbert Action important?

The Einstein-Hilbert Action is important because it provides a mathematical framework for understanding the behavior of gravity and its effects on the universe. It has been used to make predictions about the behavior of objects in space and has been confirmed by numerous experiments and observations.

3. What does the Einstein-Hilbert Action equation represent?

The Einstein-Hilbert Action equation represents the total energy of a system in terms of the curvature of space and time. It is derived from the principle of least action, which states that a system will follow the path of least resistance.

4. How is the Einstein-Hilbert Action related to Einstein's Theory of General Relativity?

The Einstein-Hilbert Action is the mathematical formulation of Einstein's Theory of General Relativity. It is used to describe the behavior of gravity and is based on the principle of equivalence, which states that the effects of gravity are equivalent to the effects of acceleration.

5. Can the Einstein-Hilbert Action be applied to other theories of gravity?

Yes, the Einstein-Hilbert Action can be applied to other theories of gravity, such as modified theories of gravity or theories that incorporate additional dimensions. However, it may need to be modified to account for these different theories and their specific predictions.

Similar threads

I Normalization Constant in Einstein-Hilbert Action
    • Special and General Relativity
Replies
10
Views
1K
A Einstein Hilbert action integral
    • Special and General Relativity
Replies
32
Views
4K
I Einstein's Derivation of Elapsed Time for Remote Comoving Object
    • Special and General Relativity
Replies
1
Views
1K
I Noether's second theorem: two questions
    • Special and General Relativity
Replies
7
Views
1K
Please help me understand time dilation
    • Special and General Relativity
2
Replies
61
Views
3K
I Deriving vacuum FRW equations directly from action
    • Special and General Relativity
Replies
1
Views
787
Hilbert-Einstein action, total derivative vanish
    • Special and General Relativity
Replies
6
Views
2K
I Benefits & Disadvantages of Palatini Action for General Relativity
    • Special and General Relativity
Replies
2
Views
1K
The factor of 1/2 in the Einstein-Hilbert action
    • Special and General Relativity
Replies
2
Views
1K
I Understanding Einstein's second postulate of special relativity
    • Special and General Relativity
2
Replies
57
Views
4K

Hot Threads

Recent Insights

Back
Top