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

Thanks.

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- Thread starter shahbaznihal
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- #1

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

Thanks.

- #2

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https://en.wikipedia.org/wiki/Palatini_variation

- #3

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There is no "spacetime fabric"...inspired by the main theme of spacetime fabric

- #4

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Yes, I have read that article but it does elaborate much on it.

https://en.wikipedia.org/wiki/Palatini_variation

I am looking for ideas and suggestion which are accepted in the scientific literature.There is no "spacetime fabric"...

- #5

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You were the one who mentioned "spacetime fabric" in the OP; that's why @weirdoguy pointed out that that's not an accepted concept.I am looking for ideas and suggestion which are accepted in the scientific literature.

- #6

haushofer

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Which models precisely are you talking about in your opening post? What are your references? :)

- #7

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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?Which models precisely are you talking about in your opening post? What are your references? :)

- #8

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Hi,You were the one who mentioned "spacetime fabric" in the OP; that's why @weirdoguy pointed out that that's not an accepted concept.

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

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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.In the classical GR space time is manifold. Hence the use of the word spacetime fabric

- #10

atyy

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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.

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.

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- #11

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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 whetherI assumed (incorrectly may be) weirdoguy is talking about some fictional ideas that spacetime as a continuous manifold does not exist. I guess, my bad?

- #12

haushofer

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That's motivated mathematically, as far as i know,not physically. In the end the connection still depends on the metric.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?

- #13

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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

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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.

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

Thanks.

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For example, check out "The theory of gravitational actions" (https://www.springer.com/us/book/9788847026919)

Now, once you understand the basics of the theory, a good paper to check out is: https://arxiv.org/pdf/1606.08756.pdf

- #16

martinbn

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This is a popular exposition. So it doesn't count.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.

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