The Birth of Einstein's General Relativity of the Gravitational Field
Metric Engineering Investigations 1.8
Landau & Lifshitz "Classical Theory of Fields" p. 228 explicitly say that the guv curved metric form is only for a non-inertial frame not an inertial frame. Since in 82 they are still operating in global special relativity they do not distinguish global from local noninertial frames at this stage in their pedagogical exposition:
"Thus, in a noninertial system of reference the square of the interval appears as a quadratic form of general type in the coordinate differentials, that is, it has the form
ds^2 = gikdx^idx^k (82.1)
i,k = 0,1,2,3
... Thus, when we use a noninertial system, the four-dimensional coordinate system x^0,x^1,x^2,x^3 is curvilinear. The quantities gik, determining all the geometric properties in each curvilinear system of coordinates, represent, we say, the space-time metric."
Many mathematicians have careers in relativity without paying attention to the measurement theory behind the formalism. Each choice of non-inertial coordinates is a possible physical configuration of detectors requiring non-gravity forces to sustain. For example, in the vacuum black hole Schwarzschild solution where, outside the event horizon where gtt = 0:
gtt = - grr^-1 = (1 - 2GM/c^2r)
2GM/c^2r < 1
Where A = 4pir^2 is area of sphere concentric with origin behind the event horizon
These are HOVERING REST LNIF observers that must fire their rockets toward the event horizon to maintain constant r. That is, they must fire rockets in order to stay still relative to the curvature field. This would not happen in flat Minkowski spacetime where the rocket would move away from say a flat Black Monolith from Kubrick's 2001 floating in space. The one exception seems to be the "curvature without curvature" effect from a highly unstable antigravitating thin wall of dark energy given by Vilenken 1983 with Taub's comment that the local conformal vacuum curvature is zero even though HOVERING observers need to fire their propellant away from the thin wall in order to keep a fixed distance from it. R. Kiehn points out that the LC connection field as a Cartan 1-form like any p-form splits into 3 pieces
Connection 1-form = Exact 1-form + Closed Non-Exact 1-form + Non-Closed 1-Form.
Curvature 2-form = d(Connection 1-form) = d(Non-Closed 1-Form) =/= 0 LOCALLY
However, Kiehn also mentions that the GLOBAL Closed Non-Exact 1-form describes topological defects like the Wilson loops for the dynamical nonlocal Bohm-Aharonov phase and presumably the anholonomic Berry phase that seem to give Taub's "curvature without curvature"? Since the smooth fabric of curved spacetime emerges from the single-valued local macro-quantum vacuum coherent world hologram Goldstone phase field with topological defects from the vanishing of its Higgs amplitude, local effects with nonlocal causes on the large-scale should be prevalent like the vortices in superfluid helium. Or so it appears with the dark matter Galactic Halo and the NASA Pioneer gravity anomaly of homogeneous a_g = -cH = 10^-7 cm/sec^2 starting 20 AU out from Sun - exactly like an S^2 hedgehog point topological defect in the vacuum coherence at the center of the Sun (David Thouless "Nonrelativistic Topological Quantum Mechanics Ch 1).
It is obvious, that in the full context of GR's LOCAL EEP L&L use "Galilean" the way MTW use "LIF" i.e. "In an inertial reference system, when we use Cartesian space coordinates, x^1,^2,^3 = x,y,z, and the time x^0 = ct,
goo = 1, g11 = g22 = g33 = -1, gik = 0 when i =/= k
we call a four-dimensional system with these values of gik 'Galilean'" p. 228
In Galilean relativity: "A noninertial system of reference is equivalent to a certain field of force. We now see that in (special) relativistic mechanics, these (inertial) fields are determined by the quantities gik."
Zielinski has been trying to keep a "Victorian Station Master's" ledger on just what is the "phony" gravity from the arbitrary contingent acceleration of the non-inertial frame and what is the "true" gravity from the non-contingent intrinsic curvature of the fabric of spacetime. Is that possible?
* Note that our alleged alien super-technologists in their magnificent unconventional flying machines having their way with us genetically for thousands of years, we call them Jehovah etc. The Many Masks of The Wizard of Oz with the Big Black Eyes and the spindly legs and arms
are able to metric engineer the intrinsic geometry in their geodesic gliders (AKA "G-Engines" George Trimble, "acceleration fields" Paul Hill) to their will so that what we think of as "intrinsic" they think of as "contingent". A similar problem was posed by Eugene Wigner in the distinction between contingent initial conditions for the early universe and the intrinsic laws of nature. Wheeler even questions that split in his "Law without law" that we now see in Lenny Susskind's "Anthropic Landscape" making a virtue of the vice of M-Theory's lack of falsifiabilty. To such depths have The Pundits descended. :-)
Now L&L start to shift to the full GR paradigm almost imperceptibly at first.
"The same applies to 'actual' gravitational fields. Any gravitational field is just a change in the metric of spacetime as determined by the quantities gik." In ADM's canonical method gik splits into a spacelike 3-geometry with 3 shift and 1 lapse function (from local gauging of the translations) to push the time evolution of the geometrodynamic field 3-geometry forward. GCT Diff(4) requires that the physics be independent of the way of slicing. Also one needs to use an infinite dimensional superspace where each 3-geometry 3g is a "point". The same is done with the EM field Fuv in the Bohmian hidden variable version of quantum field theory. The latter is no good for practical computations however. We must still fall back on Feynman diagrams for number crunching the sorts of things Victorian Station Masters want to know. However, as Mussolini's legacy we must have the trains run on time. ;-)
Enter Einstein's Geometrodynamics (incompatible irreconcilable differences with Hal Puthoff's PV metric engineering in Eric Davis's USAF "Teleportation" paper and the NIDS "High Strangeness" UFO paper and the recent Journal Interplanetary Physics paper etc): "This important fact means that the geometrical properties of spacetime (its metric) are determined by physical phenomena, and are not fixed properties of spacetime."
Note that Alex Poltorak's method of restoring locality to gravity energy seems to demand a fundamental violation of Einstein's general relativity principle because Alex invokes a "rigid nondynamical affine connection" in contrast to the non-rigid dynamical Levi-Civita connection of Einstein's 1916 GR. I say "seems" because I do not, as yet, understand what Alex is really proposing.
Zielinski's claim that the Golden Age of Soviet Physics under the aegis of Landau eschewed Einstein at least in V.A. Fock's "meta-theoretics" is certainly not justified in Landau & Lifshitz's "The theory of gravitational fields, constructed on the basis of the theory of relativity, is called the general theory of relativity. It was established by Einstein (and finally formulated by him in 1916), and it represents probably the most beautiful of all existing physical theories. It is remarkable that it was developed by Einstein in a purely deductive manner and only later was substantiated by astronomical observations."
Note that Landau does not say that David Hilbert thought of it first nor does he say that Einstein's first wife Mileva thought of it first.