The definition of energy and enegry flux of a cylindrical symmetric system in general relativity is given by Kip Throne in Phys. Rev. 138, B251 and generalized by Chandrasekhar in Proc. Roy. Soc. Lond. A 408, 209 (1986) for non-diagonal case so called C-energy and C-enegry flux.
My question is whether this derivation of enegry could be generalized to define the (conserved) angular monmentum of a infinitely Long, cylindrically symmetric systems in general relativity ?