: on one side Minkowski space is described as hyperbolic, and deSitter space is (hyper)spherical. Both are used, yet how can you have spacetime being both hyperbolic and spherical?Minkowski spacetime is a flat, four-dimensional spacetime that obeys special relativity. It has zero curvature and is often used to describe the motion of objects in the absence of gravity. On the other hand, deSitter spacetime is a curved, four-dimensional spacetime that obeys general relativity. It has positive curvature and is often used to describe the expansion of the universe.
Minkowski spacetime has a hyperbolic geometry, which means that the angles of a triangle add up to less than 180 degrees. On the other hand, deSitter spacetime has a spherical geometry, which means that the angles of a triangle add up to more than 180 degrees.
Minkowski spacetime is more commonly used in physics because it is simpler and easier to work with. It is also the basis for special relativity, which is a fundamental theory in physics. However, deSitter spacetime is also used in certain areas of physics, such as cosmology.
Yes, it is possible to combine Minkowski and deSitter spacetime to create a hybrid model known as Minkowski-deSitter spacetime. This model is often used in cosmology to describe the universe at different stages of its evolution.
Since Minkowski and deSitter spacetime have different geometries, they affect the behavior of matter and energy differently. In Minkowski spacetime, matter and energy follow straight lines and move at constant velocities. In deSitter spacetime, matter and energy are affected by the curvature of spacetime and may follow curved paths or accelerate due to the presence of gravity.