4 ms·
It's less about the metric but the choice of space/time decomposition.
by cygx 7y ago
It's less about the metric but the choice of space/time decomposition.
- 6gvONxR4sf7o 7y agoI'm not talking about a metric over space, but rather a metric over spacetime, if that's what you mean. I would consider that to encode the space/time decomposition. My differential geometry sucks, but I thought you could write general relativity in a coordinate free manner that specifically doesn't rely on strong coordinate choices like you're talking about.
- cygx 7y agoI thought you could write general relativity in a coordinate free manner that specifically doesn't rely on strong coordinate choices Indeed. But even before you start messing with the formalism, the metric alone cannot be used to define a speed as 4-velocities are normalized. You need to decompose your tangent space into timelike and spacelike subspaces so you can have a dx and a dt.