Frame fields in general relativity

Imagine that you are sitting in a car and someone is driving you around. The car is moving, but you are staying still inside it. Now, imagine that instead of a car, you are in a spaceship traveling through space. In both cases, you feel like you are not moving, but that's because your body is just following the motion of the vehicle around you.

In the same way, objects and people on Earth feel like they are not moving, but in reality, the Earth is spinning and orbiting around the Sun, which is itself moving around the center of the Milky Way galaxy. So, we need to be able to describe motion in a way that takes into account the fact that everything is actually moving through space and time.

This is where the idea of frame fields comes in. A frame field is a way of describing how objects move through space and time in a given region of the universe. It is like a set of reference points that allow us to measure motion and change.

In the theory of general relativity, frame fields are particularly important because they help us to describe the curvature of spacetime. According to this theory, gravity is not a force that pulls objects towards each other, but rather a curvature of spacetime caused by the presence of matter and energy.

To describe this curvature mathematically, we need to use a frame field that takes into account the motion of objects and light in the presence of a gravitational field. This frame field allows us to measure the curvature of spacetime and predict how objects will move in that region of space.

So, just like the reference points in the car or the spaceship allowed us to measure motion, frame fields allow us to measure the curvature of spacetime caused by gravity. By understanding how frame fields work, we can better understand the way that gravity affects the motion of objects throughout the universe.