Sure, relativity is filled with quantities that are the same in each good reference frame. These are called "invariants". Einstein at one point tried to rename the theory "invariants theory" but by then the name "relativity" had stuck.
Here's two examples, drawn from special relativity (I don't know general relativity well enough to give ones from it):
d
2-c
2t
2 where d is the distance between two events, t is the time interval between them, and c is the speed of light.
E
2-p
2c
2 , where E is the total energy of some stuff and p is its total momentum.
Note that the constant speed of light is just a special case of the first invariant, one where the invariant value happens to be zero.
Mike W.
(published on 12/10/2012)