Future and past timelike infinity are ideal endpoints of asymptotically escaping timelike trajectories in a conformal completion. For the Minkowski conformal compactification, they are the vertices and ; these vertices are not physical spacetime events.
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Timelike infinity is a concept primarily found in the field of general relativity and mathematical physics. It refers to a point or a boundary in spacetime where time-like paths (paths that can be traversed by massive particles) converge as one moves toward the infinite future or past.