In flat spacetime what we say that something (energy, information, charge, whatever) is conserved we take some region of space at moment t1, check the amount of that something, then we count the amount of the same thing at t2. What is ‘at moment t1’? It means that we cut spacetime using 2 spacelike surfaces (t1 and t2), and separate some region of space using closed 3d timelike surface. There are some specific requirements for t1 and t2 surfaces; the improper choice of the shape of these surfaces leads to non-conservation; for example, energy is not conserved in cosmology, because cosmological time t is bent surface. My question is, what is a general definition for ‘is conserved’ in curved spacetimes? For example, in Closed Time-like Loops? Is charge ‘conserved’ in such metrics? Say, charge enters the proximity or Kerr singularity, orbits 3 times around the ring, and escapes to CTL-free region. Local observer can see 3 'copies' of the same charge at the same time. How is it interpreted?