Question: What frames do light propogate like it does in special relativity?
About the article "General relativity", section "Relativistic generalization".

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As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of (special) relativistic mechanics.
In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics.
(The defining symmetry of special relativity is the Poincaré group which also includes translations and rotations.)
The differences between the two become significant when we are dealing with speeds approaching the speed of light, and with high-energy phenomena.
With Lorentz symmetry, additional structures come into play.
They are defined by the set of light cones (see the image on the left).
The light-cones define a causal structure: for each event A, there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light (such as event B in the image), and a set of events for which such an influence is impossible (such as event C in the image).
These sets are observer-independent.
In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the space–time's semi-Riemannian metric, at least up to a positive scalar factor.
In mathematical terms, this defines a conformal structure.
Special relativity is defined in the absence of gravity, so for practical applications, it is a suitable model whenever gravity can be neglected.
Bringing gravity into play, and assuming the universality of free fall, an analogous reasoning as in the previous section applies: there are no global inertial frames.
Instead there are approximate inertial frames moving alongside freely falling particles.
Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.
A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity hold—that theory is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames.
But using different assumptions about the special-relativistic frames (such as their being earth-fixed, or in free fall), one can derive different predictions for the gravitational redshift, that is, the way in which the frequency of light shifts as the light propagates through a gravitational field (cf.
below).
The actual measurements show that free-falling frames are the ones in which light propagates as it does in special relativity.
The generalization of this statement, namely that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames, is known as the Einstein equivalence principle, a crucial guiding principle for generalizing special-relativistic physics to include gravity.
The same experimental data shows that time as measured by clocks in a gravitational field—proper time, to give the technical term—does not follow the rules of special relativity.
In the language of spacetime geometry, it is not measured by the Minkowski metric.
As in the Newtonian case, this is suggestive of a more general geometry.
At small scales, all reference frames that are in free fall are equivalent, and approximately Minkowskian.
Consequently, we are now dealing with a curved generalization of Minkowski space.
The metric tensor that defines the geometry—in particular, how lengths and angles are measured—is not the Minkowski metric of special relativity, it is a generalization known as a semi- or pseudo-Riemannian metric.
Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection, and this is, in fact, the connection that satisfies the equivalence principle and makes space locally Minkowskian (that is, in suitable locally inertial coordinates, the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish).
As formulated by Albert Einstein in 1905, the theory of special relativity was based on two main postulates:  The principle of relativity — The form of a physical law is the same in any inertial frame.
The speed of light is constant — In all inertial frames, the speed of light c is the same whether the light is emitted from a source at rest or in motion.
(Note this does not apply in non-inertial frames, indeed between accelerating frames the speed of light cannot be constant.
Although it can be applied in non-inertial frames if an observer is confined to making local measurements.)
There have been various alternative formulations of special relativity over the years.
Some of these formulations are equivalent to the original formulation whereas others result in modifications. 
End of aether?Special Relativity.
Aether theory was dealt another blow when the Galilean transformation and Newtonian dynamics were both modified by Albert Einstein's special theory of relativity, giving the mathematics of Lorentzian electrodynamics a new, "non-aether" context.
Unlike most major shifts in scientific thought, special relativity was adopted by the scientific community remarkably quickly, consistent with Einstein's later comment that the laws of physics described by the Special Theory were "ripe for discovery" in 1905.
Max Planck's early advocacy of the special theory, along with the elegant formulation given to it by Minkowski, contributed much to the rapid acceptance of special relativity among working scientists.
Einstein based his theory on Lorentz's earlier work.
Instead of suggesting that the mechanical properties of objects changed with their constant-velocity motion through an undetectable aether, Einstein proposed to deduce the characteristics that any successful theory must possess in order to be consistent with the most basic and firmly established principles, independent of the existence of a hypothetical aether.
He found that the Lorentz transformation must transcend its connection with Maxwell's equations, and must represent the fundamental relations between the space and time coordinates of inertial frames of reference.
In this way he demonstrated that the laws of physics remained invariant as they had with the Galilean transformation, but that light was now invariant as well.
With the development of the special relativity, the need to account for a single universal frame of reference had disappeared — and acceptance of the 19th century theory of a luminiferous aether disappeared with it.
For Einstein, the Lorentz transformation implied a conceptual change: that the concept of position in space or time was not absolute, but could differ depending on the observer's location and velocity.
Moreover, in another paper published the same month in 1905, Einstein made several observations on a then-thorny problem, the photoelectric effect.
In this work he demonstrated that light can be considered as particles that have a "wave-like nature".
Particles obviously do not need a medium to travel, and thus, neither did light.
This was the first step that would lead to the full development of quantum mechanics, in which the wave-like nature "and" the particle-like nature of light are both considered to be descriptions of the same thing.
A summary of Einstein's thinking about the aether hypothesis, relativity and light quanta may be found in his 1909 (originally German) lecture "The Development of Our Views on the Composition and Essence of Radiation".
Lorentz on his side continued to use the aether concept.
In his lectures of around 1911 he pointed out that what "the theory of relativity has to say ... can be carried out independently of what one thinks of the aether and the time".
He commented that "whether there is an aether or not, electromagnetic fields certainly exist, and so also does the energy of the electrical oscillations" so that, "if we do not like the name of "aether", we must use another word as a peg to hang all these things upon."
He concluded that "one cannot deny the bearer of these concepts a certain substantiality". 
  In 1889, (Henri Poincaré argued that the ether might be unobservable, in which case the existence of the ether is a metaphysical question, and he suggested that some day the ether concept would be thrown aside as useless.
However, in the same book (Ch.
10) he considered the ether a "convenient hypothesis" and continued to use the concept also in later papers in 1908 ([Poi08, Book 3) and 1912 (, Ch.
6).
In 1895, Poincaré argued that experiments like that of Michelson–Morley show that it seems to be impossible to detect the absolute motion of matter or the relative motion of matter in relation to the ether.
In he called this the Principle of Relative Motion, i.e., that the laws of movement should be the same in all inertial frames.
Alternative terms used by Poincaré were "relativity of space" and "principle of relativity".
In 1904 he expanded that principle by saying: ""The principle of relativity, according to which the laws of physical phenomena must be the same for a stationary observer as for one carried along in a uniform motion of translation, so that we have no means, and can have none, of determining whether or not we are being carried along in such a motion.""
However, he also stated that we do not know if this principle will turn out to be true, but that it is interesting to determine what the principle implies.
In , Poincaré published a paper in which he said that radiation could be considered as a fictitious fluid with an equivalent mass of formula_1.
He derived this interpretation from Lorentz's 'theory of electrons' which incorporated Maxwell's radiation pressure.
Poincaré had described a synchronization procedure for clocks at rest relative to each other in and again in [Poi04.
So two events, which are simultaneous in one frame of reference, are not simultaneous in another frame.
It is very similar to the one later proposed by Einstein.
However, Poincaré distinguished between "local" or "apparent" time of moving clocks, and the "true" time of resting clocks in the ether.
In [Poi02 he argued that "some day, no doubt, the ether will be thrown aside as useless".
Lorentz' paper containing the transformations bearing his name appeared in 1904.
Albert Einstein in derived the Lorentz equations by using the principle of constancy of velocity of light and the relativity principle.
He was the first to argue that those principles (along with certain other basic assumptions about the homogeneity and isotropy of space, usually taken for granted by theorists) are sufficient to derive the theory.
See Postulates of special relativity.
He said: ""The introduction of a "luminiferous ether" will prove to be superfluous inasmuch as the view here to be developed will not require an "absolutely stationary space" provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.""
* Einstein's "Elektrodynamik" paper [Ein05c contains no formal references to other literature.
It does mention, in §9, part II, that the results of the paper are in agreement with Lorentz's electrodynamics.
Poincaré is not mentioned in this paper, although he is cited formally in a paper on special relativity written by Einstein the following year.
In 1905 Einstein was the first to suggest that when a material body lost energy (either radiation or heat) of amount formula_2, its mass decreased by the amount formula_3.
Hermann Minkowski showed in 1907 that the theory of special relativity could be elegantly described using a four-dimensional spacetime, which combines the dimension of time with the three dimensions of space.
Einstein in 1920 returned to a concept of aether having no state of motion.  
Einstein developed special relativity on the basis of two postulates: First postulate – Special principle of relativity – The laws of physics are the same in all inertial frames of reference.
In other words, there are no privileged inertial frames of reference.
Second postulate – Invariance of "c" – The speed of light in a vacuum is independent of the motion of the light source.
Special relativity can be derived from these postulates, as was done by Einstein in 1905.
Einstein's postulates are still applicable in the modern theory but the origin of the postulates is more explicit.
It was shown above how the existence of a universally constant velocity (the speed of light) is a consequence of modeling the universe as a particular four-dimensional space having certain specific properties.
The principle of relativity is a result of Minkowski structure being preserved under Lorentz transformations, which are "postulated" to be the physical transformations of inertial reference frames.