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According to Newton's emission theory of light, light slows down in
the gravitational field of the emitter and continues to move
REDSHIFTED in the distant (zero-field) space with a DECREASED speed
c'=c(1+phi/c^2), where phi is the gravitational potential difference
between the surface of the emitter and the distant (zero-field) space.

According to Einstein's relativity, light slows down even more
vigorously in the gravitational field of the emitter and continues to
move EVEN MORE REDSHIFTED in the distant (zero-field) space with an
EVEN LOWER speed c'=c(1+2phi/c^2):

http://www.mathpages.com/rr/s6-01/6-01.htm
"In geometrical units we define c_0 = 1, so Einstein's 1911 formula
can be written simply as c=1+phi. However, this formula for the speed
of light (not to mention this whole approach to gravity) turned out to
be incorrect, as Einstein realized during the years leading up to 1915
and the completion of the general theory. In fact, the general theory
of relativity doesn't give any equation for the speed of light at a
particular location, because the effect of gravity cannot be
represented by a simple scalar field of c values. Instead, the "speed
of light" at a each point depends on the direction of the light ray
through that point, as well as on the choice of coordinate systems, so
we can't generally talk about the value of c at a given point in a non-
vanishing gravitational field. However, if we consider just radial
light rays near a spherically symmetrical (and non- rotating) mass,
and if we agree to use a specific set of coordinates, namely those in
which the metric coefficients are independent of t, then we can read a
formula analogous to Einstein's 1911 formula directly from the
Schwarzschild metric. (...) In the Newtonian limit the classical
gravitational potential at a distance r from mass m is phi=-m/r, so if
we let c_r = dr/dt denote the radial speed of light in Schwarzschild
coordinates, we have c_r =1+2phi, which corresponds to Einstein's 1911
equation, except that we have a factor of 2 instead of 1 on the
potential term."

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German (download from:
http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1911_35_898-908.pdf
). It predated the full formal development of general relativity by
about four years. You can find an English translation of this paper in
the Dover book 'The Principle of Relativity' beginning on page 99; you
will find in section 3 of that paper Einstein's derivation of the
variable speed of light in a gravitational potential, eqn (3). The
result is: c'=c0(1+phi/c^2) where phi is the gravitational potential
relative to the point where the speed of light co is measured......You
can find a more sophisticated derivation later by Einstein (1955) from
the full theory of general relativity in the weak field
approximation....For the 1955 results but not in coordinates see page
93, eqn (6.28): c(r)=[1+2phi(r)/c^2]c. Namely the 1955 approximation
shows a variation in km/sec twice as much as first predicted in 1911."

Apart from the gravitational redshift, light seems to slow down (and
so gets additionally redshifted) even in the absence of a
gravitational field, due to "friction" with some unknown components of
"empty" space. Naturally, this (Hubble) redshift is proportional to
the distance. Einsteinians have found it profitable to explain Hubble
redshift not in terms of slowing down of the speed of light but,
rather, in terms of an accelerating expansion of the universe. Given
the perfect discipline in Einsteiniana, hints at slowing down of the
speed of light in empty space never come from Einsteinians. There was
one exception (now suppressed):

http://www.sciscoop.com/2008/10
"Does the apparently constant speed of light change over the vast
stretches of the universe? Would our understanding of black holes,
ancient supernovae, dark matter, dark energy, the origins of the
universe and its ultimate fate be different if the speed of light were
not constant?.....Couldn't it be that the supposed vacuum of space is
acting as an interstellar medium to lower the speed of light like some
cosmic swimming pool? If so, wouldn't a stick plunged into the pool
appear bent as the light is refracted and won't that affect all our
observations about the universe. I asked theoretical physicist Leonard
Susskind, author of The Black Hole War, recently reviewed in Science
Books to explain this apparent anomaly....."You are entirely right,"
he told me, "there are all sorts of effects on the propagation of
light that astronomers and astrophysicists must account for. The point
of course is that they (not me) do take these effects into account and
correct for them." "In a way this work is very heroic but unheralded,"
adds Susskind, "An immense amount of extremely brilliant analysis has
gone into the detailed corrections that are needed to eliminate these
'spurious' effects so that people like me can just say 'light travels
with the speed of light.' So, there you have it. My concern about
cosmic swimming pools and bent sticks does indeed apply, but
physicists have taken the deviations into account so that other
physicists, such as Susskind, who once proved Stephen Hawking wrong,
can battle their way to a better understanding of the universe."

Pentcho Valev
pvalev@yahoo.com