Hello Bishal Banjara,

You mention the rubber sheet as in many popular views of curved spacetime. How can it be that in that curved sheet an object traces a circle around the central object? The object is moving along a surface with a slope towards the central object. Why would it start to move to the centre? we assume in that analogy that there is a gravitational force waking vertical down. Now we can sum the force down with the upward force of the surface and get a vector sum force inward to the centre. With enough forward speed we can get an orbital speed that generates a centrifugal force that is equal to inward force and, voila, we have something that resembles the orbit of a planet. What to do if we want to tilt the rotation axis? Then we have to to tilt our gravity with it. This means that for each Cartesian plane through the centre we have to have concentric circles with for each circle a special slope attached. As long as the object resides in one plane we have to assume a gravity perpendicular to that. when it moves to another plane we have to move the gravity direction. We can solve this situation when we state that this force is originating from a 4th dimension orthogonal to the there space dimensions. Now where is this great attractor?

Also, in geometric gravity theories there is the assumption that space can curve. Base on the equivalence principle that an acceleration force can't be distinguished from a gravitational force we have the problem that we try to make a curved force field equal to a flat force field. If we want that a curved field looks flat we can do that if we define the space coordinates as curved. You can try that with a curved line on a paper. To make this curved line become a straight line in another paper you put that other paper orthogonal on the first paper. Then you can trace the curve in the first paper with the edge of the second paper. This means you need for any curve an orthogonal help space. These help spaces are the solution of your equations. They are not the real space but the orthogonal help space where in that point of your equation the local curved field appears as flat.

Real space does not bend, the help spaces bend. They are the product of mathematical calculations and can have whatever attributes you might want to give them. But for every new point you will need another help space. So your fabric of space is the intersection of all these help spaces over all the points. They describe a slope with respect to the central mass based on an assumed perpendicular attraction force from an assumed 4th dimension attractor. If this sounds weird to you then I agree with you.

Regards,

Paul Gradenwitz

Ok, your answer is based on Mass reference than space-time reference. Let we are in perfect empty space-time without any mass disturbances, than the orientation of planes of space-time could also be choose to linked to 4 pie angle substension or there is not only a fixed preferred plane as a reference but taking Minkowski line element (for inertial case) we could or should have to take a single plane only, at a time. And the result doesn't guaranty to be only single kind of such plane around. How would you interpret it, now?

Hi Bishal

Are you concerned with some kind of classical spacetime fluctuations in the strong gravity domain in the vicinity of a huge mass? Classical spacetime fluctuations, instead of quantum fluctuations, appear in the very interesting approach developed by Walter Greiner and Peter Hess - pseudo-complex general relativity.

Hello Cesar,

Its definitely not because, their paper is concerned about say, simply that how strong the field (assume gravitational) is proportional to the mimicking of space time fluctuations and apparently one may stuck on this regard to my question but what I am actually expecting is the frame tackling pedagogy to refer or set in around such mass, and also to the region where there is no mass. see the last comment of mine just above yours on Paul's comment.

Hi Bishal

Without mass no curvature, no gravity, no gravity variation, no fluctuations...frame tackling pedagogy (?)...i have difficulties to follow you on basis of our (present) knowledge on general relativity...

ok, I will make a very simplified way to express what I mean. Suppose, I lean a rubber sheet parallel to horizontal axis. Let a high densed mass is kept on the center of sheet and it will create a depression around that mass from the central orientation, as usually. This plane of sheet represents the linearized Schwarzschild solution. But there is no fixed frame or say the horizontal axis we assumed is not universal or say absolute, such selection of axis could be done in multiple ways of angular variance around that mass or in 4 pie angle substension, though this perspective such linearized plane could be taken as isolative solution with parallel to horizontal axis but to be general due to not fixed or absolute frame of reference, we may have or say nature may not work on such isolation rather a multiple options of such occurrence, in general. This manifests that if such linearized plane would be accumulated around that mass in 4 pie angle substension, it will result a spherical depression of fabric of space-time around any kind of mass taken in reference instead of such rubber sheet analogy. Your initial quest was addressed about the density or say number of linearized plane existed within or say such fabric compilation (like the number of rubber sheet beneath the mass M within certain range), I think.

My question is not addressed to any presently existed norms in GR but it expects more than that.....thank you for your enthusiasm.

Dear Bishal

Did you realize you stablished this way an absolut referencial frame, ab initio, the rubber...? This is completely inconsistent with GR...and GR is the best theory for such staff we know...

Nope, I have not such intention, and I am not getting on your point " .... you stablished this way an absolut referencial frame.... " I am not evoking about absolute reference but against of it.

Hello Sydney,

It's something like that but I think its not to the complete what I meant. Will you give me the original source on this regards? I didn't see it in the same page on wiki.

:- )