How does closed timelike curve work?

In a closed timelike curve, the worldline of an object through spacetime follows a curious path where it eventually returns to the exact same coordinates in space and time that it was at previously. In other words, a closed timelike curve is the mathematical result of physics equations that allows for time travel.

How do you make a closed timelike curve?

A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started.

Do all objects follow geodesics?

It is this curvature of spacetime that gives rise to what we interpret as gravitational acceleration. Note that there is no mass in this equation – it doesn’t matter what the mass of the object is, they all follow the same geodesic (so long as it’s not massless, in which case things are a little different).

Are geodesics straight?

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines.

What is a closed timelike curve in physics?

In a closed timelike curve, the worldline of an object through spacetime follows a curious path where it eventually returns to the exact same coordinates in space and time that it was at previously. In other words, a closed timelike curve is the mathematical result of physics equations that allows for time travel.

Can black holes have closed timelike curves?

In the 1960s, solutions to the field equations were found that describe not only stationary black holes, but also black holes that are rotating or spinning. To the surprise of many, these solutions appear to show that the space and time immediately surrounding a rotating black hole can also contain closed timelike curves.

What happens to the light cone in curved spacetime?

In curved spacetimes the light cone will be “tilted” along the spacetime’s geodesic. For instance, while moving in the vicinity of a star, the star’s gravity will “pull” on the object, affecting its worldline, so its possible future positions lie closer to the star. This appears as a slightly tilted lightcone on the corresponding spacetime diagram.

What are timelike and spacelike events?

Any single point on such a diagram is known as an event. Separate events are considered to be timelike separated if they differ along the time axis, or spacelike separated if they differ along the space axis.