Introduction to the mathematics of general relativity: Difference between revisions

Revision as of 00:08, 19 December 2019

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A good example of this is the surface of the Earth. While maps frequently portray north, south, east and west as a simple square grid, that is not in fact the case. Instead, the longitude lines running north and south are curved and meet at the north pole. This is because the Earth is not flat, but instead round.

In general relativity, energy and mass have curvature effects on the four dimensions of the universe (called= spacetime). This curvature gives rise to the gravitational force. A common analogy is placing a heavy object on a stretched out rubber sheet, causing the sheet to bend downward. This curves the coordinate system around the object, much like an object in the universe curves the coordinate system it sits in. The mathematics here are conceptually more complex than on Earth, as it results in [[Four-dimensional space|four dimensions]] of curved coordinates instead of three as used to describe a curved 2D surface.

==Parallel transport==