Locally Flat Spacetime
Strictly speaking, the use of the Minkowski space to describe physical systems over finite distances applies only in the Newtonian limit of systems without significant gravitation. In the case of significant gravitation, spacetime becomes curved and one must abandon special relativity in favor of the full theory of general relativity.
Nevertheless, even in such cases, Minkowski space is still a good description in an infinitesimal region surrounding any point (barring gravitational singularities). More abstractly, we say that in the presence of gravity spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space. Thus, the structure of Minkowski space is still essential in the description of general relativity.
In the realm of weak gravity, spacetime becomes flat and looks globally, not just locally, like Minkowski space. For this reason Minkowski space is often referred to as flat spacetime.
Read more about this topic: Minkowski Space
Famous quotes containing the words locally and/or flat:
“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”
—Clifford Geertz (b. 1926)
“We say justly that the weak person is flat, for, like all flat substances, he does not stand in the direction of his strength, that is, on his edge, but affords a convenient surface to put upon. He slides all the way through life.... But the brave man is a perfect sphere, which cannot fall on its flat side and is equally strong every way.”
—Henry David Thoreau (1817–1862)