Why GRT is the proper correction of gravitomagnetism?

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The best experimental tests of the general relativity: of frame dragging by Gravity Probe B, use calculations from approximation of GRT, called gravitomagnetism: http://en.wikipedia.org/wiki/Gravitoelectromagnetism
It was originally introduced by Oliver Heaviside in 1893 as expansion of Newton's gravity to Lorentz invariant theory by analogue of Maxwell equations. The correction is that while rotating charge creates magnetism, rotating mass creates analogous effects, like frame dragging.

I wanted to ask about the arguments, experimental evidence/suggestions that gravitomagnetism is not the end of the story and we need higher order terms of GRT?
The huge freedom of local behavior of the spacetime makes GRT non-renormalizable ... while electromagnetism and so gravitomagnetism are renormalizable - maybe for the unification it would be better to focus on some simpler higher order terms?
 

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Bill_K
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Linear gravity does not have black hole solutions.
 
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Indeed, they don't allow for point singularity in the center of black hole ... but honestly GRT also doesn't allow it as the spacetime is no longer a manifold there - we are getting out of applicability of the theory.

We know that there exist large mass concentrations, like Sagittarius A* for which we can limit density from below by 0.0066 kg/m^3, but what is the evidence that their internal structure agrees with GRT?
 
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Nugatory
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I wanted to ask about the arguments, experimental evidence/suggestions that gravitomagnetism is not the end of the story and we need higher order terms of GRT?
The huge freedom of local behavior of the spacetime makes GRT non-renormalizable ... while electromagnetism and so gravitomagnetism are renormalizable - maybe for the unification it would be better to focus on some simpler higher order terms?
I understand that Heaviside's theory is not Lorentz-invariant, which greatly reduces its appeal as an end of the story.
 
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?
Gravitomagnetism is the simplest expansion of Newton's gravity to make it Lorentz-invariant.
In exactly the same way as we make Coulomb force Lorentz-invariant: by adding magnetism and corresponding Maxwell equations.
 
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Bill_K
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We know that there exist large mass concentrations, like Sagittarius A* for which we can limit density from below by 0.0066 kg/m^3, but what is the evidence that their internal structure agrees with GRT?
Here, for example, is a NASA press release reporting experimental evidence for the presence of an event horizon.
 
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From this NASA article:
"By comparing the energy output of different types of X-ray novae while they were inactive, the Chandra team determined that systems suspected of harboring black holes emitted only one percent as much energy as systems with neutron stars. "
One explanation could be some less active version of neutron star ...
But let us assume that it is indeed the event horizon - does it imply the GRT?
Does it even imply the intrinsic curvature of spacetime? (leading to non-renormaizability, getting out of the theory in the center of black holes, allowing for wormholes, requiring existence of further dimensions...).
Why it cannot be just local rotations/deformations of light cones - that spacetime is flat and only space is curved (submanifolds of constant time)?
 
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Gravitomagnetism is the simplest expansion of Newton's gravity to make it Lorentz-invariant.
In exactly the same way as we make Coulomb force Lorentz-invariant: by adding magnetism and corresponding Maxwell equations.
Nugatory is correct, it is not Lorentz invariant. The problem is the source terms. They don't transform correctly. At least that is my understanding, I haven't actually worked it out myself.
 
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I don't understand?
If you see electrodynamics as Lorentz invariant, gravitomagnetism is mathematically nearly the same (there is sign change to make the same mass attracting).

Sure there are probably needed some higher order corrections to the confirmed by Gravity Probe B gravitomagnetism, but the question is why there is belief that they have to be chosen in non-renormalizable: GRT way?
 
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Ben Niehoff
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Ok, the second link indeed contains a problem ... but not exactly with Lorentz invariance, but rather with lack of direct compatibility with the stress-energy tensor: containing densities, pressures - complex effective properties.
Like for electromagnetism, it is Lorentz invariant while considering point particles ... but indeed we should be more careful while extending it to densities.

What I don't like in Einstein's aesthetic assumption of intrinsic curvature - not only of space (local light cones), but also of the whole spacetime (and haven't seen reasons for):
- it makes GRT non-renormalizable, extremely resistant to any trials of unifications (while gravitomagnetism seems to naturally unify with EM),
- it requires additional dimensions. For example surface of constant positive curvature encloses into a sphere, requiring 3rd dimension: toward the center. If there would be additional dimensions, any interaction would make that our heat would escape there, what should be observed. It also means that spacetime remains infinitely thin in higher dimensional space - what enforces it to have zero thickness? In perpendicular line, spacetime would be a discontinuity,
- it allows for black holes with singularities in the center, where spacetime is no longer a manifold (becomes sharp spike), allows for wormholes which theoretically could destroy orientability (if glued like in Klein bottle) ...
 
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