Gravitational Time Dilation

Do you know what happened in the movie 'Interstellar', when the protagonist returned from his voyage and found that his daughter was even older than him? Well, I'll tell you how that happened. 

You all must be familiar with the name of the famous scientist Albert Einstein, he was the one who suggested that space and time are interrelated where space is the three-dimensional world we live in. both of them are together termed as four-dimensional spacetime. Every object in the spacetime curves it.  The heavier the object, the greater is the curve. This is what we call warping of spacetime. Let's take the example of putting a ball on a bedsheet. When we stretch the bedsheet and put a ball on it, we'll observe that it creates a curve at that place and the heavier the ball, the larger is the curve.

 The warping of spacetime is the reason that the earth revolves around the sun because mas of the earth is comparatively very small than that of the sun, so the sun creates a huge warp in the spacetime causing the Earth to eventually revolve around it as the warp of Earth is much smaller than the warp of Sun. 

Now the question is why doesn't the Earth bump into the Sun? The answer is simple. It's because the Earth has also deformed the spacetime a little bit and hence maintains its balance. This states that a massive object warps the spacetime more so its gravitational force will be larger or in other words, greater the gravitational force, greater will be the warping of spacetime. In the same way, a black hole is much more massive than the stars with a very high gravitational field that even light can't escape from there. thus, it creates a huge warp in the spacetime continuum. 

Let me explain you with the help of an example. Suppose we have to move in spacetime from point A to point B and from point C to point D, where points A and B are in less warped region, and points C and D are in the more warped region.

We all know the simple equation the speed=distance/time, where the speed of light is always the same equal to 299,792,458m/s, which means that time is directly proportional to distance when speed is constant. So this indicates that in a more warped region of spacetime i.e. in the area of strong gravitational force the distance of traveling increases and thus time being directly proportional to distance, increases. Hence, showing that in the region of a strong gravitational field, time slows down. This is what is called Gravitational Time Dilation. 

And this is what happened in the movie 'Interstellar', the protagonist went to a planet which was very near to a black hole where time slowed down for him but not for the people who were on Earth because they were in a weak gravitational field as compared to the Black Hole. That's why when he returned, his daughter was older than him.

So now I don't think you have any confusion about what Gravitational Time Dilation is. And this is also the reason why the Earth's core is approximately 2.5 years younger than its surface because Earth's gravitational force decreases as you move away from the center of Earth and yeah this is also the reason your feet are slightly younger than your head.