On metric and connection independence

  • #1
Some models of gravity, inspired by the main theme of spacetime fabric of Classical GR, treat the metric of the manifold and the connection as independent entities. I want to study this theory further but I am unable to find any paper on this, on ariXiv atleast.

I will be very thankful if someone can provide reference to such a paper.

Thanks.
 

Answers and Replies

  • #3
664
496
inspired by the main theme of spacetime fabric
There is no "spacetime fabric"...
 
  • #5
PeterDonis
Mentor
Insights Author
2020 Award
32,969
11,445
I am looking for ideas and suggestion which are accepted in the scientific literature.
You were the one who mentioned "spacetime fabric" in the OP; that's why @weirdoguy pointed out that that's not an accepted concept.
 
  • #6
haushofer
Science Advisor
Insights Author
2,479
866
Which models precisely are you talking about in your opening post? What are your references? :)
 
  • #7
Which models precisely are you talking about in your opening post? What are your references? :)
For example in one version of Platini formulation of gravity the metric and connections are taking as independent quantities. I know there are many other. But I am interested in understanding the physical motivation of such a step?
 
  • #8
You were the one who mentioned "spacetime fabric" in the OP; that's why @weirdoguy pointed out that that's not an accepted concept.
Hi,

In the classical GR space time is manifold. Hence the use of the word spacetime fabric. Other ideas where spacetime is treated as discrete points is not what I was talking about. I assumed (incorrectly may be) weirdoguy is talking about some fictional ideas that spacetime as a continuous manifold does not exist. I guess, my bad?
 
  • #9
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,829
6,652
In the classical GR space time is manifold. Hence the use of the word spacetime fabric
I do not see the implication. "Fabric" has nothing to do with being a manifold, it is something typically made up by popular science descriptions.
 
  • Like
Likes dextercioby
  • #10
atyy
Science Advisor
14,319
2,552
http://space.mit.edu/LIGO/more.html
Gravitational Waves: Ripples in the fabric of space-time
Albert Einstein predicted the existence of gravitational waves in 1916 as part of the theory of general relativity. In Einstein's theory, space and time are aspects of a single measurable reality called space-time. Matter and energy are two expressions of a single material. We can think of space-time as a fabric; The presence of large amounts of mass or energy distorts space-time – in essence causing the fabric to "warp" – and we observe this warpage as gravity. Freely falling objects – whether soccer balls, satellites, or beams of starlight – simply follow the most direct path in this curved space-time.

@stevendaryl gave the correct answer in post #2. A useful reference might be Sotiriou, 6+1 lessons from f(R) gravity, https://arxiv.org/abs/0810.5594.
 
Last edited:
  • #11
PeterDonis
Mentor
Insights Author
2020 Award
32,969
11,445
I assumed (incorrectly may be) weirdoguy is talking about some fictional ideas that spacetime as a continuous manifold does not exist. I guess, my bad?
Yes. While the term "spacetime fabric" does appear in some sources (such as the one @atyy linked to), it's generally best to avoid using that term, precisely because it makes it unclear whether you are talking about standard GR or about other speculative ideas about spacetime. @weirdoguy was not talking about such speculative ideas himself; he was unclear about whether you were.
 
  • #12
haushofer
Science Advisor
Insights Author
2,479
866
For example in one version of Platini formulation of gravity the metric and connections are taking as independent quantities. I know there are many other. But I am interested in understanding the physical motivation of such a step?
That's motivated mathematically, as far as i know,not physically. In the end the connection still depends on the metric.
 
  • #13
robphy
Science Advisor
Homework Helper
Insights Author
Gold Member
5,779
1,078
Possibly useful:

https://www.physicsforums.com/threa...ic-compatible-connection.199500/#post-1512119

https://www.physicsforums.com/threa...a-metric-compatible-affine-connection.761642/

https://physics.stackexchange.com/questions/212298/how-to-measure-torsion-and-non-metricity

[i haven’t read this:] “The role of nonmetricity in metric-affine theories of gravity”
http://iopscience.iop.org/article/10.1088/0264-9381/31/4/045006
https://arxiv.org/abs/1308.1642


One reason there may be interest in alternative formulations is that they may be easier to generalize for a quantum theory of gravity, which may or may not respect torsion-free metric compatibility (assuming such structures exist there).
 
  • #14
samalkhaiat
Science Advisor
Insights Author
1,721
1,003
Some models of gravity, inspired by the main theme of spacetime fabric of Classical GR, treat the metric of the manifold and the connection as independent entities. I want to study this theory further but I am unable to find any paper on this, on ariXiv atleast.

I will be very thankful if someone can provide reference to such a paper.

Thanks.
Search for "First order formulation", there are countless number of paper on the subject. In GR, first order formalism is also known as the Palatini formulation.
 
  • #16
martinbn
Science Advisor
2,123
700
http://space.mit.edu/LIGO/more.html
Gravitational Waves: Ripples in the fabric of space-time
Albert Einstein predicted the existence of gravitational waves in 1916 as part of the theory of general relativity. In Einstein's theory, space and time are aspects of a single measurable reality called space-time. Matter and energy are two expressions of a single material. We can think of space-time as a fabric; The presence of large amounts of mass or energy distorts space-time – in essence causing the fabric to "warp" – and we observe this warpage as gravity. Freely falling objects – whether soccer balls, satellites, or beams of starlight – simply follow the most direct path in this curved space-time.
This is a popular exposition. So it doesn't count.
 
  • Like
Likes Demystifier and weirdoguy

Related Threads on On metric and connection independence

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
9
Views
603
Replies
94
Views
7K
Replies
78
Views
11K
Replies
2
Views
2K
Top