Episode 136: Introduction to General Relativity
The Science of Everything Podcast
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The Covariant Derivative and Einstein's Field Equations
In Einstein's field equations we have to do more mathematical work and introduce something called the covariant derivative. It factors in incorporates the fact that the space itself has changed as you've moved from one position into anotherSpace itself has curved so you have to factor this in when an object moves from one position to another The object might have moved or changed or rotated but it's also possible that it's just space that's curved. You need to separate out those two effects now we can figure out ways of doing this mathematically.
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