Yes, gravity does affect the speed of light. According to Einstein's general theory of relativity, gravity is not just a force but rather the curvature of spacetime caused by massive objects. In the presence of a gravitational field, the path of light is influenced, resulting in changes in its speed.
In a region with a strong gravitational field, such as near a massive object like a black hole, the speed of light is affected. The theory predicts that light will follow a curved path in the presence of gravity, causing it to appear slower or faster depending on the observer's position relative to the gravitational field.
Specifically, gravitational time dilation occurs, which means that time appears to pass slower in a stronger gravitational field compared to a weaker field. This effect is caused by the curvature of spacetime and affects the propagation of light as well.
For example, light passing through a strong gravitational field will experience a gravitational redshift, where its frequency decreases and its wavelength becomes longer. This corresponds to a decrease in the perceived speed of light. On the other hand, light moving away from a gravitational field will experience a blueshift, where its frequency increases, and its wavelength becomes shorter, corresponding to an increase in the perceived speed of light.
In summary, gravity does have an impact on the speed of light due to the curvature of spacetime caused by massive objects.