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- Question about the definition of future null infinity

So I was trying to get a bit better handle on the definition of the difference between an event horizon and a Killing horizon. Locally they are indistinguishable, and the key difference (to my understanding) is that the event horizon is the last Killing horizon that escapes to future null infinity.

But I have found the concept of future null infinity a bit confusing. I believe that it is the set of all events in spacetime that are at the end of a null geodesic as the affine parameter goes to infinity. I have two specific concerns about this concept

1) I don't understand what is meant by the end of a geodesic as the affine parameter goes to infinity. In what way does an infinite line have an end?

2) Does this definition of future null infinity include the events on the photon sphere where the affine parameter goes to infinity as the null geodesic is a helix that loops around the circumference of the photon sphere an infinite number of times?

But I have found the concept of future null infinity a bit confusing. I believe that it is the set of all events in spacetime that are at the end of a null geodesic as the affine parameter goes to infinity. I have two specific concerns about this concept

1) I don't understand what is meant by the end of a geodesic as the affine parameter goes to infinity. In what way does an infinite line have an end?

2) Does this definition of future null infinity include the events on the photon sphere where the affine parameter goes to infinity as the null geodesic is a helix that loops around the circumference of the photon sphere an infinite number of times?