Special and general relativity

Question

Is the light postulate in special relativity (that the speed of light is constant in all frames of reference) correct if the equivalence principle shows that light slows down in gravitational field?

Would this then not make Elevator thought experiment a "destructive" and "constructive" thought experiment since it invalidates an existing postulate or theory.

Please see James Robert Brown of 'The Laboratory of The Mind', page 34, who makes the distinction between destructive and constructive thought experiments. The distinction is also provided in the following article: https://plato.stanford.edu/entries/thought-experiment/#TypThoExpTax

Relevant: https://physics.stackexchange.com/q/59502/ – InertialObserver Dec 29 '18 at 20:02 — InertialObserver, Dec 29 '18 at 20:02
But light isn't slower locally right? – BioPhysicist Dec 29 '18 at 20:03 — BioPhysicist, Dec 29 '18 at 20:03

G. Smith · Answer 1 · 2018-12-29T20:16:13.223

General Relativity does not invalidate Special Relativity; it only restricts its realm of applicability. Just as the curved surface of the Earth seems flat to us if we don’t venture too far, curved spacetime is also locally flat, or Minkowskian, so Special Relativity applies locally everywhere (except at singularities) even though it does not apply globally.

Even in a strong gravitational field such as near a black hole, nearby inertial observers moving relative to each other will all see nearby light moving with speed $c$.

Mathematically, a curved $n$-dimensional Riemannian manifold has a flat $n$-dimensional tangent space at each point. Special Relativity applies to physics restricted to any such tangent space.

Special and general relativity

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