synge

Even with a broader definition of local, a Synge 5-point like process is not going to find a failure of parallel transport in a sufficiently small region.

-- particularly the overview of the point raised by JL Synge in his textbook 1960 Relativity: The General Theory; Pub: North-Holland that one finds in one of the upvoted answers.

The symmetries of Schwarzschild and Minkowski spacetime are different, and if one were to probe the spacetimes in question with a Synge curvature detector [1], we would quickly discover which we were probing if our probes happened to be placed close to the central mass, and eventually if they were placed far from the central mass.

Synge's method) that the spacelike part of the spacetime curvature is curved and thus one is inside a truly enormous vacuum black hole.

- -- [1] Of particular (pardon the pun) interest to anyone who has read Synge's five point curvature detector.

Synge in his textbook [1] discusses a five-point curvature detector, which is the formal treatment for a small cloud of non-interacting dust that reveals the Riemann curvature tensor.

Closer observers will see (optically, even!) that it's lumpy, and if they have sufficiently sensitive gravimeters or a probe like Synge's "five-point curvature detector" they will see that Schwarzschild is not quite accurate.

[Synge 1960, Relativity: The General Theory (Amsterdam: North-Holland), ch.

Fermi coordinate are uniquely determined by a choice of pseudo-orthonormal frame along the null geodesic \gamma" "For many (in particular more advanced) purposes it is useful to rephrase the above construction of Fermi coordinates in terms of the Synge world function").

Misner, Thorne & Wheeler's _Gravitation_ has a chapter on Israel junction conditions, and various authors notably Darmois, O'Brien, Synge, Bonnor and Raju have catalogued stitchings of different types of metrics into one another.

That's fine; it's really hard for general relativity to confront observation without doing some splitting, and implicitly threading is standard behaviour (Synge does this in his textbook, for example, when discussing 3-velocity and spatial distance and offering up his world function biscalar; note that this is different from explicitly applying a 1+3 formalism).

Closer observers will see (optically, even!) that it's lumpy, and if they have sufficiently sensitive gravimeters or a probe like Synge's "five-point curvature detector" they will see that Schwarzschild is not quite accurate.

Fermi coordinate are uniquely determined by a choice of pseudo-orthonormal frame along the null geodesic \gamma" "For many (in particular more advanced) purposes it is useful to rephrase the above construction of Fermi coordinates in terms of the Synge world function").

Synge's method) that the spacelike part of the spacetime curvature is curved and thus one is inside a truly enormous vacuum black hole.

- -- [1] Of particular (pardon the pun) interest to anyone who has read Synge's five point curvature detector.

Synge in his textbook [1] discusses a five-point curvature detector, which is the formal treatment for a small cloud of non-interacting dust that reveals the Riemann curvature tensor.