In the vicinity of closed timelike curves tend to be non-closed curves which could provide useful delivery. Blackholes may not be exited either but the concept of extracting energy from the ergosphere is still a useful thing.
As I understand the presence of closed timelikie curves is a classification that marks out those spacetimes that are in danger of featuring time travel. Like the coffee mug is an example of the topology that has a hole.
I think the situation is analogous in that you can draw a path on a coffemug that closes on itself but it doesn’t mean that it is impossible to make a path that enters and exits the handle. Such a path is possible and need not be closed (within the handle).
(say if one consider the bottom of the mug to be deep past and the top of it to be deep future, the time trallers path would be open but the possib lity of such paths is conected to the existence of the “handle” but the actual travel doesn’t actually take place on the round going part of it)
No, it is literally impossible to enter or exit a CTC, at least in classical GR. All CTCs are shrouded by a Cauchy horizon, meaning that you cannot “push” the evolution of a spatial slice into a CTC region. Or out of it, if you apply the same logic in reverse. The issue most people forget is that the spacetime in GR is not a background on which matter exists, the spacetime metric is unique (up to diffeomorphisms) and it uniquely determines the stress energy tensor at every point in spacetime, which means it determines its matter content almost completely. Thus one cannot have one loop of a CTC without something being there, and another with it. Anyway, it’s getting a bit technical. My original comment was that the OP setup breaks physics as we know it, and so it’s kind of pointless to discuss.
In the vicinity of closed timelike curves tend to be non-closed curves which could provide useful delivery. Blackholes may not be exited either but the concept of extracting energy from the ergosphere is still a useful thing.
No, there is no such thing as a “vicinity” of closed timelike curves. They are causally isolated from the rest of the spacetime.
As I understand the presence of closed timelikie curves is a classification that marks out those spacetimes that are in danger of featuring time travel. Like the coffee mug is an example of the topology that has a hole.
I think the situation is analogous in that you can draw a path on a coffemug that closes on itself but it doesn’t mean that it is impossible to make a path that enters and exits the handle. Such a path is possible and need not be closed (within the handle).
(say if one consider the bottom of the mug to be deep past and the top of it to be deep future, the time trallers path would be open but the possib lity of such paths is conected to the existence of the “handle” but the actual travel doesn’t actually take place on the round going part of it)
No, it is literally impossible to enter or exit a CTC, at least in classical GR. All CTCs are shrouded by a Cauchy horizon, meaning that you cannot “push” the evolution of a spatial slice into a CTC region. Or out of it, if you apply the same logic in reverse. The issue most people forget is that the spacetime in GR is not a background on which matter exists, the spacetime metric is unique (up to diffeomorphisms) and it uniquely determines the stress energy tensor at every point in spacetime, which means it determines its matter content almost completely. Thus one cannot have one loop of a CTC without something being there, and another with it. Anyway, it’s getting a bit technical. My original comment was that the OP setup breaks physics as we know it, and so it’s kind of pointless to discuss.