What mathematical quantity can characterise the extent of twisting at “twisting singular points”?
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Recently, inspired by the phenomenon of frame dragging of spacetime around rotating massive bodies, I became curious on how to characterise how much a surface locally twists
For example, in this photo, the whole surface of the towel is twisted around a point at the white stick
It seems curvature tensor alone is insufficient to describe the twisting behaviour in the neighbourhood of the point. What else can be used to further characterise points like these?
Also I like to know about the characterisation of these twisting points in general, thus I am not limited to lorentzian or riemannian spaces
geometry singularity
asked Dec 9 '18 at 2:07
SecretSecret
1,0951020
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add a comment |
$begingroup$
Recently, inspired by the phenomenon of frame dragging of spacetime around rotating massive bodies, I became curious on how to characterise how much a surface locally twists
For example, in this photo, the whole surface of the towel is twisted around a point at the white stick
It seems curvature tensor alone is insufficient to describe the twisting behaviour in the neighbourhood of the point. What else can be used to further characterise points like these?
Also I like to know about the characterisation of these twisting points in general, thus I am not limited to lorentzian or riemannian spaces
geometry singularity
asked Dec 9 '18 at 2:07
SecretSecret
1,0951020
$endgroup$
$begingroup$
How is it not similar to the (geodesics in) Schwarzschild metric ?
$endgroup$
– reuns
Dec 9 '18 at 3:33
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Isn't the schwarzchild metric does not involve any rotation hence twisting?
$endgroup$
– Secret
Dec 9 '18 at 4:58
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This is my limited qualitative understanding. By far the larger effect is that rotation in space is to the first order of approximation absolute as shown by the Sagnac experiment. The frame dragging effect is the theory that rotation is not quite absolute it also depends on the mass of the rotating body (in isolation perhaps or alternatively in combination somehow with the distributed mass of the rest of the universe [Mach's principle]) . In my opinion as both effects must be measured using light you have to take account of the two effects to give a correct mathematical description.
$endgroup$
– James Arathoon
Dec 9 '18 at 11:22
add a comment |
$begingroup$
Recently, inspired by the phenomenon of frame dragging of spacetime around rotating massive bodies, I became curious on how to characterise how much a surface locally twists
For example, in this photo, the whole surface of the towel is twisted around a point at the white stick
It seems curvature tensor alone is insufficient to describe the twisting behaviour in the neighbourhood of the point. What else can be used to further characterise points like these?
Also I like to know about the characterisation of these twisting points in general, thus I am not limited to lorentzian or riemannian spaces
geometry singularity
asked Dec 9 '18 at 2:07
SecretSecret
1,0951020
$endgroup$
Recently, inspired by the phenomenon of frame dragging of spacetime around rotating massive bodies, I became curious on how to characterise how much a surface locally twists
For example, in this photo, the whole surface of the towel is twisted around a point at the white stick
It seems curvature tensor alone is insufficient to describe the twisting behaviour in the neighbourhood of the point. What else can be used to further characterise points like these?
Also I like to know about the characterisation of these twisting points in general, thus I am not limited to lorentzian or riemannian spaces
geometry singularity
geometry singularity
asked Dec 9 '18 at 2:07
SecretSecret
1,0951020
asked Dec 9 '18 at 2:07
SecretSecret
1,0951020
edited Dec 9 '18 at 11:27
Secret
asked Dec 9 '18 at 2:07
SecretSecret
1,0951020
asked Dec 9 '18 at 2:07
SecretSecret
1,0951020
asked Dec 9 '18 at 2:07
SecretSecret
1,0951020
1,0951020
$begingroup$
How is it not similar to the (geodesics in) Schwarzschild metric ?
$endgroup$
– reuns
Dec 9 '18 at 3:33
$begingroup$
Isn't the schwarzchild metric does not involve any rotation hence twisting?
$endgroup$
– Secret
Dec 9 '18 at 4:58
$begingroup$
This is my limited qualitative understanding. By far the larger effect is that rotation in space is to the first order of approximation absolute as shown by the Sagnac experiment. The frame dragging effect is the theory that rotation is not quite absolute it also depends on the mass of the rotating body (in isolation perhaps or alternatively in combination somehow with the distributed mass of the rest of the universe [Mach's principle]) . In my opinion as both effects must be measured using light you have to take account of the two effects to give a correct mathematical description.
$endgroup$
– James Arathoon
Dec 9 '18 at 11:22
add a comment |
$begingroup$
How is it not similar to the (geodesics in) Schwarzschild metric ?
$endgroup$
– reuns
Dec 9 '18 at 3:33
$begingroup$
Isn't the schwarzchild metric does not involve any rotation hence twisting?
$endgroup$
– Secret
Dec 9 '18 at 4:58
$begingroup$
This is my limited qualitative understanding. By far the larger effect is that rotation in space is to the first order of approximation absolute as shown by the Sagnac experiment. The frame dragging effect is the theory that rotation is not quite absolute it also depends on the mass of the rotating body (in isolation perhaps or alternatively in combination somehow with the distributed mass of the rest of the universe [Mach's principle]) . In my opinion as both effects must be measured using light you have to take account of the two effects to give a correct mathematical description.
$endgroup$
– James Arathoon
Dec 9 '18 at 11:22
$begingroup$
How is it not similar to the (geodesics in) Schwarzschild metric ?
$endgroup$
– reuns
Dec 9 '18 at 3:33
$begingroup$
How is it not similar to the (geodesics in) Schwarzschild metric ?
$endgroup$
– reuns
Dec 9 '18 at 3:33
$begingroup$
Isn't the schwarzchild metric does not involve any rotation hence twisting?
$endgroup$
– Secret
Dec 9 '18 at 4:58
$begingroup$
Isn't the schwarzchild metric does not involve any rotation hence twisting?
$endgroup$
– Secret
Dec 9 '18 at 4:58
$begingroup$
This is my limited qualitative understanding. By far the larger effect is that rotation in space is to the first order of approximation absolute as shown by the Sagnac experiment. The frame dragging effect is the theory that rotation is not quite absolute it also depends on the mass of the rotating body (in isolation perhaps or alternatively in combination somehow with the distributed mass of the rest of the universe [Mach's principle]) . In my opinion as both effects must be measured using light you have to take account of the two effects to give a correct mathematical description.
$endgroup$
– James Arathoon
Dec 9 '18 at 11:22
$begingroup$
This is my limited qualitative understanding. By far the larger effect is that rotation in space is to the first order of approximation absolute as shown by the Sagnac experiment. The frame dragging effect is the theory that rotation is not quite absolute it also depends on the mass of the rotating body (in isolation perhaps or alternatively in combination somehow with the distributed mass of the rest of the universe [Mach's principle]) . In my opinion as both effects must be measured using light you have to take account of the two effects to give a correct mathematical description.
$endgroup$
– James Arathoon
Dec 9 '18 at 11:22
add a comment |
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$begingroup$
How is it not similar to the (geodesics in) Schwarzschild metric ?
$endgroup$
– reuns
Dec 9 '18 at 3:33
$begingroup$
Isn't the schwarzchild metric does not involve any rotation hence twisting?
$endgroup$
– Secret
Dec 9 '18 at 4:58
$begingroup$
This is my limited qualitative understanding. By far the larger effect is that rotation in space is to the first order of approximation absolute as shown by the Sagnac experiment. The frame dragging effect is the theory that rotation is not quite absolute it also depends on the mass of the rotating body (in isolation perhaps or alternatively in combination somehow with the distributed mass of the rest of the universe [Mach's principle]) . In my opinion as both effects must be measured using light you have to take account of the two effects to give a correct mathematical description.
$endgroup$
– James Arathoon
Dec 9 '18 at 11:22