Teleportation violates conservation of energy?

[Superposed_Cat]

Hi, GR permits wormholes hypothetically right? But surely they should violate conservation of energy
because if one were to put one mouth in the ground an the other in the sky then you could enerate infinite energy by continually falling through them. Am I wrong? any help appreciated.

 

[WannabeNewton]

Solutions to Einstein's equation always satisfy $\nabla^a T_{ab} = 0$ (local energy conservation), including wormhole solutions. Global energy conservation cannot be defined unless the solution is stationary.