I read (I think ) that part of relativity theory is that a strong gravitational field distorts the uniform passage of time. If this is true and a lightwave 'travelling' to Earth passes a star near its intense gravitational field (a gravity 'lens') does the gravitational field distort the 'timing' of the speed of light and for a small duration of time the light-wave slows a bit until it leaves the influence of the star's gravity? If this is so could you say the speed of light itself was slightly less while the lightwave was passing through the star's gravity?
We need to be a bit cautious about making over simplified statements in this area because it is a minefield for the unwary. However it is true that as observed by observers far from the star, the gravitional field does affect the elapsed time for objects within it and it also affects the distances travelled by those objects. The net result is that the speed of light does vary with distance from the star.
For more details you might want to look at the questions Photons emitted at the event horizon? and Speed of light originating from a star with gravitational pull close to black-hole strength? for a more detailed discussion of this.
The time dilation is a real effect and has been experimentally measured. In 1971 Hafele and Keating measured the affect of the Earth's gravity on atomic clocks. You ask about this in your comment to user3138766's answer, and the answer is that the time dilation slows everything. If you hovered near a black hole for a while then returned to Earth you would find you were younger than your contemporaries on Earth.
Gravitational lensing is due to the curvature of spacetime. The change in the speed of light in effect changes the refractive index of the space it's travelling through, and this bends the light in an analogous way to the bending of light by a lens.
Gravitational fields in space distort light. The speed of light is constant, so if light is passing through this gravitational field, it does not slow down but rather time itself relative to the observer, slows down. This is how Einstein explained how the speed of light is constant, regardless of other acting forces.
Constant $c$ is the framework of entire Relativistic Physics. You start from here. Meaning, any Time Dilation is derived from constant $c$. You can't go in reverse to alter $c$ using Time Dilation.
Think it another way: When you say someone's time is dilated, you actually compare results of own reference frame to the results of that someone's reference frame. For photons, reference frame isn't defined because there's no reference frame in which photons are at rest. So, you can't really calculate time dilation for photons.
Note: This is a strong answer. Any other answer saying different thing is plain simple wrong.
For fun, if you think about Time Dilation for photons, it's already dilated to Infinity whether it's in Gravity well or not (remember, time is dilated due to speed and they have got topmost speed possible). Now, how much further would you like to push dilation using Gravity?
Time appears to slow down as light passes a strong object of gravity. Time is not really a physical property, time is simply a unit of measure invented by earthlings.
Time appears to change because gravity bends light and it actually travels further to get to the observer so it takes longer to get there.
Time is actually distance travelled. The light that was headed straight for us was bent and crashed into the source of gravity, the light we see was actually headed at a slight angle away from us and it was then bent toward us taking the longer route.
If there is an increasing redshift of light as it moves further away from mass and a center of gravity, and a blueshift when light moves in towards the same center of gravity, the only possible explanation is that a photon has to accelerate to match the speed of mass. Since a photon is massless it cannot fall into a gravity well, and without mass a blueshift can only be caused by increased speed. As a photon is separated from mass and there is a redshift, the conclusion must be that mass has higher speed than light.
If time dilate with increased gravity, remembering that time dilates with increasing speed, gravity would be connected to mass being accelerated to a higher speed than the surrounding space and pulling the fabric of spacetime.
I agree with time being a subjective local perspective of distance travelled, as the only real difference between two points in time is change in position in relation to surrounding bodies in space.
If time is distance travelled, and time dilate with increasing gravity, distance dilate with increased mass because increasing mass is basically an increase in speed. When a photon blushifts approaching mass, it is caused by the acceleration needed to catch up with mass.
Is it possible that light doesn´t move? And the constant property of energy as light, actually is the relation between accelerated mass and static energy, with light being the transformation of energy into mass as it is accelerating?
There is no denying that any mass has the energy of being accelerated to squared lightspeed. No mass is at rest. I see no way around the obvious conclusion that increasing mass is increasing acceleration, and that the energy that is the origin of light is at rest.
Then gravity is similar to the effect on your body as it is pushed against the seat in an accelerating car. Not an attracting property, but inertia of matter in relation to acceleration. More like pressure.
Mass exhibit properties that could be expected from Special relativity if we interpret E=mc^2 literally as mass always being the accelerated state and massless energy stands still. If c^2 is constant, then mass is nothing but a measure of light being accelerated. Isn´t that correct?
It is the only possible solution, since mass is only increase in energy in relation to c. Mass is c accelerating if c is constant without mass.
Gravity must be the inertia of the massless universe interacting with a point where there is a difference in speed of mass and light. The force acts in direction of acceleration, just like gravity acts attracting towards increasing mass.
What is the reason for interpreting E=mc^2 as the energy needed for acceleration of mass to lightspeed squared, instead of accepting the fact that all mass must exist in a state of c^2 since it´s energy is equal to that acceleration?
If mass emerged after the initial expansion of big bang, the acceleration was already achieved when mass condensed in spacetime. The only way mass can have the energy of m*c^2 is if it emerged after acceleration was a fact, since the energy needed for accelerating mass to c^2 is unrealisticly large.
If energy is equal to mass at c^2, then there is no doubt that mass travels at c^2. And gravity must be the difference in energy from the difference in speed between points of different density of mass.Acceleration is movement towards higher density, as time dilate then also distance travelled has to dilate, which must be connected to increasing speed, which makes gravity part of the same energytransformation that is always present in the relation between light and matter. A geometric volume, like a gravity well, seems like a perfect expression of how energy transforms by stretching out(dilating) space time when there is an acceleration directed towards a point in otherwise uniform space.