Intro

Image courtesy of mathoverflow.net

To understand General Relativity fully, we are required to reach beyond the mathematics of Euclidean space and into the world of Differential Geometry.

Differential geometry brings the tools of differential calculus, linear algebra, multilinear algebra, and integral calculus to bear on geometric problems. Something gained from these areas of study is how to deal with curved spaces.

When dealing with curved space, we must define what a flat space (flat here meaning non-curved). A good example of a flat (Euclidean) space is the x-y coordinate axis, which doesn’t contain too many surprises (as long as we keep things two-dimensional).

A depiction of Euclidean space. Image courtesy of http://math.tutorvista.com/algebra/Euclidean-space.html

But space-time, we will see eventually, can be curved.

A depiction of curved space. Image courtesy of http://www.quantum-field-theory.net/space-time-curvature-relativity/

It is my goal to give an explanation of the mathematics involved in understanding general relativity, but not take you through a semester of differential calculus or linear algebra. Where possible, I will post links to more, in-depth information.


DOWN THE RABBIT HOLE!

Some Background