In the presence of gravity, time does not slow down in the same way that light warps. Instead, it's more accurate to say that time itself is affected by gravity and behaves differently in regions of different gravitational fields.
According to Einstein's theory of general relativity, gravity is not seen as a force in the traditional sense, but rather as the curvature of spacetime caused by massive objects. This curvature affects the geometry of spacetime, including the flow of time.
In the vicinity of a massive object, such as a planet or a black hole, the gravitational field is stronger, and this leads to a slowing down of time relative to an observer in a weaker gravitational field. This effect is known as gravitational time dilation.
Gravitational time dilation can be understood using the concept of spacetime curvature. Massive objects create a "dent" in the fabric of spacetime, causing it to curve. As a result, the path of an object, including light, passing through this curved spacetime gets bent or warped. Light follows the curvature of spacetime, which gives the impression of warping.
However, for an observer experiencing time, the effect of gravity is different. In a region of stronger gravity, where spacetime is more curved, time runs slower relative to a region with weaker gravity. This means that clocks closer to a massive object tick more slowly compared to clocks farther away. This phenomenon has been observed in various experiments and is consistent with the predictions of general relativity.
To summarize, gravity affects the geometry of spacetime, causing light to follow curved paths, while time itself is influenced by the gravitational field, resulting in gravitational time dilation where time appears to run slower in regions of stronger gravity.