Alright, I'm rather new to General Relativity, and I'm getting confused with four momentum. Back in SR, [itex]p^α=mU^α[/itex], but, this relationship doesn't hold in curved space, does it? Because, now I'm seeing that four momentum is somehow a covector in GR, and [itex]p_0=-E[/itex], so the time component of the contravariant component can't be E, since the 00 component of the metric isn't always -1. So, is four momentum now redefined in GR, and if the SR relationship between four velocity isn't valid, what is the new relationship to U? Is four momentum naturally a covariant thing?