# Special and general relativity

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

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.