[naasking]

General relativity doesn't conserve energy in some spacetimes, so it's not unheard of.

[andrewflnr]

I'm fairly certain GR conserves momentum, even if it doesn't conserve energy.

[naasking]

I thought so too until recently, but in GR energy and momentum are unified in an energy-momentum metric which is only locally conserved [1].

[1] https://en.wikipedia.org/wiki/Physical_theories_modified_by_...