This relativistic, time-travel spacetime is everywhere metrically flat, excepting a conical singularity. Observers following timelike geodesics can eventually encounter their past selves, aging in the opposite time sense. The spacetime is not time orientable.
REFERENCES
1.
2.
3.
“
Reply to criticisms
,” in Albert Einstein-Philosopher Scientist
, edited by
P. A.
Schilpp
(
The Library of Living Philosophers
,
Evanston, Illinois
, 1949
), pp. 687
–88
.4.
Kurt
Gödel
, “
An example of a new type of cosmological solutions of Einstein's field equations of gravitation
,” Rev. Mod. Phys.
21
(3
), 447
–450
(1949
).5.
For reviews, see
John
Earman
,
Christian
Wüthrich
, and
J. B.
Manchak
, “
Time machines
,” The Stanford Encyclopedia of Philosophy
, edited by
Edward N.
Zalta
(2022
). <https://plato.stanford.edu/archives/spr2022/entries/time-machine>;Christopher
Smeenk
,
Frank
Arntzenius
, and
Tim
Maudlin
, “
Time travel and modern physics
,” The Stanford Encyclopedia of Philosophy
, edited by
Edward N.
Zalta
and
Uri
Nodelman
(2023
). <https://plato.stanford.edu/archives/spr2023/entries/time-travel-phys/>.6.
Michael S.
Morris
,
Kip S.
Thorne
, and
Ulvi
Yurtsever
, “
Wormholes, time machines, and the weak energy condition
,” Phys. Rev. Lett.
61
(13
), 1446
–1449
(1988
).7.
Frank J.
Tipler
, “
Rotating cylinders and the possibility of global causality violation
,” Phys. Rev. D
9
(8
), 2203
–2206
(1974
).8.
See Sec. III in
George F. R.
Ellis
and
B. G.
Schmidt
, “
Singular spacetimes
,” Gen. Relativ. Gravitation
8
(11
), 915
–953
(1977
).9.
See Sec. III B in
John D.
Norton
, “
The dome: An unexpectedly simple failure of determinism
,” Philos. Sci.
75
(5
), 786
–798
(2008
).© 2025 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2025
Author(s)
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