# Thread: Intrinsic Curvature in GR

1. As I have learned intrinsic curvature can be shown on 2 D surfaces

The spacetime model ,however is 3D+1

How ,broadly speaking is curvature assessed in that context?Are 2D surfaces within the 4D manifold drawn locally and used to make this assessment?

Are vectors"walked around" these surfaces?

2. Originally Posted by geordief
As I have learned intrinsic curvature can be shown on 2 D surfaces

The spacetime model ,however is 3D+1

How ,broadly speaking is curvature assessed in that context?Are 2D surfaces within the 4D manifold drawn locally and used to make this assessment?

Are vectors"walked around" these surfaces?
Neither. The spacetime itself (4D) is what is curved. In the presence of gravitating mass. You will need to learn differential geometry in order to understand how.

3. Originally Posted by AndrewC
Neither. The spacetime itself (4D) is what is curved. In the presence of gravitating mass. You will need to learn differential geometry in order to understand how.
Is not the curvature of space-time the "sum" of (1) the curvature along increasing time and (2) the curvature along the increasing spatial axes?

When those increments are viewed geometrically (eg x,dx :y,dy: z,dz: t ,dt) does not geometric object created by those 8 apexes have "sides" that can be called "surfaces" and doesn't each of these surfaces deform in the presence of mass-energy?

Does that geometric object conform to the spacetime distance relationship* so that its time component(s?) change by different rates than the spatial components?

*s^2 =r^2 -[ct]^2

4. Originally Posted by geordief
Is not the curvature of space-time the "sum" of (1) the curvature along increasing time and (2) the curvature along the increasing spatial axes?
No, it is not the "sum". You need to stop making guesses and you need to take a class. There is no shortcut.

It doesn't because there isn't. You need to take a class, there are no shortcuts.

5. I put sum in quotes as I did not expect their contributions to "add"

Are you saying to total spacetime curvature is not composed of its temporal and spatial parts?
"It doesn't because there isn't" is not clear to me.

They don't exist at all or just on that page?

6. Originally Posted by geordief
I put sum in quotes as I did not expect their contributions to "add"
You need to take a class and you need to stop trying to take shortcuts.

Are you saying to total spacetime curvature is not composed of its temporal and spatial parts?
I have never said that. I only pointed out that things cannot be dumbed down at the level you want them dumbed down.

7. So you are apparently saying that the spatial curvature and the temporal curvature do combine to give the total space-time curvature.

Are these components calculated separately ?

8. Originally Posted by geordief
So you are apparently saying that the spatial curvature and the temporal curvature do combine to give the total space-time curvature.

Are these components calculated separately ?
No, they are not "separate". The Einstein Field Equations are a set of coupled , non-linear differential equations.

9. But there are separate values for temporal curvature and spatial curvature.
Do these values have to be calculated out of the EFE or can they be arrived at individually in a more direct way?

10. Originally Posted by geordief
But there are separate values for temporal curvature and spatial curvature.
No.
Do these values have to be calculated out of the EFE or can they be arrived at individually in a more direct way?
No and no.
One can MEASURE spacetime curvature INDIRECTLY, though a very complicated consequence, the geodetic effect.

11. So why is it that gravity in gravity wells) is described as being more a result of the curvature of time than the curvature of space? (Pretty sure I heard that)

12. Originally Posted by geordief
So why is it that time dilation (caused by gravity wells) is described as being more a result of the curvature of time than the curvature of space? (Pretty sure I heard that)
No serious book would claim that, it is definitely false for the GPS. You need to stop trolling me and enroll in a class.

13. See I edited my post as I misspoke.Is that a better question?

14. Originally Posted by geordief
See I edited my post as I misspoke.Is that a better question?
Your edited post is just as false. You can't learn physics from internet soundbites. The time dilation falls out the solution of the EFEs. This needs to take into consideration difference in gravitational potential and difference in terms of both radial and tangential speed between two different clocks.

15. In my edited post (you answered so quickly I had not enough time to correct it ) I don't refer to time dilation but the curvature of spacetime due to gravity.

I have heard that this is more due to temporal effects than spatial effects

Does that make sense? Is it true?

I don't want to take up your time too much
We can come back to it tomorrow perhaps

16. Originally Posted by geordief
In my edited post (you answered so quickly I had not enough time to correct it ) I don't refer to time dilation but the curvature of spacetime due to gravity.

I have heard that this is more due to temporal effects than spatial effects

Does that make sense? Is it true?

I don't want to take up your time too much
We can come back to it tomorrow perhaps
In the case of geodetic effect, the time dilation contributes twice as much as the rotational effects. This is true for the case of the geodetic effect ONLY. See here for exact calculations. The language of physics is math, you need to be able to converse in that language, not in soundbites picked up from the internet. For example, the above is not true in the case of frame-dragging, another effect of spacetine curvature.

17. Originally Posted by AndrewC
In the case of geodetic effect, the time dilation contributes twice as much as the rotational effects. This is true for the case of the geodetic effect ONLY. See here for exact calculations. The language of physics is math, you need to be able to converse in that language, not in soundbites picked up from the internet. For example, the above is not true in the case of frame-dragging, another effect of spacetine curvature.
I would like to return to the OP if that is OK. I will give a different answer to your first reply and perhaps you might give an answer to it (I think I am conceding you main point I think)

18. Originally Posted by AndrewC
Neither. The spacetime itself (4D) is what is curved. In the presence of gravitating mass. You will need to learn differential geometry in order to understand how.
So are there 2D surfaces in spacetime which are used in the process of showing overall 3D+1 intrinsic curvature due to the presence of mass-energy? (say a surface with dimensions of [ct] and [x])

Can we say the spacetime curvature along the x-axis is quantitively different from that along the y- and z-axes?

19. Originally Posted by geordief
So are there 2D surfaces in spacetime which can display intrinsic curvature owing to the presence of mass-energy? (say a surface with dimensions of [ct] and [x])
This is not what GR is saying. Why do you persist?

20. Why do you jump down my throat ?Do you ever leave your device.?This is twice you have answered me so quickly before I have corrected my post(see above -again.)

This is like the spider and the fly.

I edited it to "So are there 2D surfaces in spacetime which are used in the process of showing overall 3D+1 intrinsic curvature due to the presence of mass-energy? (say a surface with dimensions of [ct] and [x])"

21. Originally Posted by geordief

Can we say the spacetime curvature along the x-axis is quantitively different from that along the y- and z-axes?
Yes, so what? Every time I correct your misconceptions you change your post. Every time I answer your ill posed questions you move the goalposts claiming "I didn't ask A, I asked B". Where are you going with that? Why do you refuse to take a class?

22. Why don't you just answer my last underlined question?(I have conceded one or two mistakes in your favour)
In case you forgot this is my OP and I have posed my question in order to learn.

Let me be the judge of "so what?".If it reinforces my understanding it is helpful to me (if apparently irritating to you)

23. Originally Posted by geordief
Why do you jump down my throat ?Do you ever leave your device.?This is twice you have answered me so quickly before I have corrected my post(see above -again.)

This is like the spider and the fly.

I edited it to "So are there 2D surfaces in spacetime which are used in the process of showing overall 3D+1 intrinsic curvature due to the presence of mass-energy? (say a surface with dimensions of [ct] and [x])"
A "2D surface with dimensions of [ct] and [x]" is a Minkowski PLANE. As such, it has ZERO curvature. So, you don't want to take a class. Why?

24. Originally Posted by AndrewC
A "2D surface with dimensions of [ct] and [x]" is a Minkowski PLANE. As such, it has ZERO curvature. So, you don't want to take a class. Why?
Really none of your business but since you have asked for the fifth or sixth time I am a poor and obtuse learner with blind spots that can impede my thinking.

I neither have the time nor the opportunity to take classes and would struggle to keep up I sure.

In my twenties this would have been easier but now(if contemplatable) it would be an all consuming commitment which would be foolish for me to undertake .

.....So a flat plane it is.Are these ([ct],[x]) flat planes ,if small enough joined together to form a curved surface in a region of spacetime?

Are they linked together in a "parallel transport" way?

EDIT:thanks for answering that last readjusted question .I realize I have no claim on your time or patience,.

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