Then why do we get galaxies in (relatively) flat discs and black holes that emit radiation in a single plane?
The concept of energy/matter deforming spacetime is a fundamental concept in Einstein's theory of general relativity. It states that the presence of energy or matter in a region of space causes a curvature in the fabric of spacetime, resulting in the warping of the geometry of space.
In three dimensions, energy/matter can be thought of as creating a dip in the fabric of spacetime, like placing a heavy object on a stretched rubber sheet. The heavier the object, the deeper the dip, and the more it distorts the surrounding space.
No, different types of energy/matter have different effects on the curvature of spacetime. For example, a massive object like a planet will have a greater effect on the warping of spacetime compared to a lighter object like a star.
One of the most well-known effects is gravitational lensing, where the path of light is bent by the curvature of spacetime around a massive object. This can result in the appearance of distorted or multiple images of distant objects. Another effect is the slowing down of time near massive objects, known as gravitational time dilation.
Yes, according to Einstein's theory of general relativity, energy/matter can cause both positive and negative curvature of spacetime. Positive curvature is associated with gravity, while negative curvature is associated with repulsive forces, such as dark energy. However, the overall curvature of spacetime is determined by the total amount and distribution of energy/matter in the universe.