A Remark on Kink and Time Machines
We describe an elementary proof that a manifold with the topology of the Politzer time machine does not admit a nonsingular, asymptotical flat Lorentz metric.
topology of the Politzer time machine Lorentz metr↗
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Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics
We explore the connections between various coordinate systems associated with observersmoving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon.We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lemaître coordinates as well.
Schwarzschild geometry↗