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Line 380: ===Curvature=== As a '''flat spacetime''', the three spatial ~~components~~directions of Minkowski spacetime always obey the [[Pythagorean Theorem]]. Minkowski space is a suitable basis for special relativity, a good description of physical systems over finite distances in systems without significant [[gravitation]]. However, in order to take gravity into account, physicists use the theory of [[general relativity]], which is formulated in the mathematics of a [[non-Euclidean geometry]]. When this geometry is used as a model of physical space, it is known as ''[[curved space]]''. Even in curved space, Minkowski space is still a good description in an [[Local reference frame\|infinitesimal region]] surrounding any point (barring gravitational singularities).<ref group=nb>This similarity between [[flat space]] and curved space at infinitesimally small distance scales is foundational to the definition of a [[manifold]] in general.</ref> More abstractly, it can be said 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.

Minkowski space: Difference between revisions