This question stems from a possibly misguided attempt to understand General Relativity. I am about to leave High school for college, I do however have a rudimentary understanding of tensors, and I have done a great deal of research into non-euclidean geometries and their extrinsic analysis over the last few months.
Using a 2 dimensional spherical geometry as an example, straight lines can be defined as great circles on the sphere representing the geometry, when embedded into a 3 dimensional euclidean geometry.
What is the equivalent definition of straight lines in the curved space-time of general relativity?
The two things I am struggling with are:
- How to imagine a 5 dimensional embedding of the 4 dimensional space-time
- How to define a straight line in geometry with somewhat random curvature (What I mean by this is that the mass distribution affects the curvature, but the mass distribution cannot be described by a "nice" mathematical function, as far as I am aware.)
I have come across the concept of Geodesics and I have read the page https://en.wikipedia.org/wiki/Geodesics_in_general_relativity and various others however, possibly unsurprisingly, I was not really able to make head or tail of it.