In an advanced course on general relativity, some exotic spacetimes like wormholes with a more complex topology than the standard Schwarzschild spacetime can be studied in detail. In this regard, it has been pointed out by Morris and Thorne that wormholes could be a valuable tool for teaching general relativity. In this paper, we claim rotating wormholes might also have a pedagogical role in general relativity, and present an empirical approach to explore periodic orbits of such, that could be applied also to other spacetimes.

1.
M. M.
Morris
and
K. S.
Thorne
, “
Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity
,”
Am. J. Phys.
56
,
395
412
(
1988
).
2.
H.
Ellis
, “
Ether flow through a drainhole: A particle model in general relativity
,”
J. Math. Phys.
14
,
104
118
(
1973
).
3.

The wormhole metric announced in the paper by Morris and Thorne (Ref. 1) should correctly be called Ellis wormhole.

4.
O.
James
,
E.
von Tunzelmann
,
P.
Franklin
, and
K. S.
Thorne
, “
Visualizing interstellar's wormhole
,”
Am. J. Phys.
83
,
486
499
(
2015
).
5.
W.
Rindler
,
Relativity—Special, General and Cosmology
(
Oxford U.P.
,
Oxford
,
2001
).
6.
E.
Teo
, “
Rotating traversable wormholes
,”
Phys. Rev. D
58
,
024014
(
1998
).
7.
T.
Müller
, “
Exact geometric optics in a Morris-Thorne wormhole spacetime
,”
Phys. Rev. D
77
,
044043
(
2008
).
8.
J.
Levin
and
G.
Perez-Giz
, “
A periodic table for black hole orbits
,”
Phys. Rev. D
77
,
103005
(
2008
).
9.
J.
Levin
and
G.
Perez-Giz
, “
Homoclinic orbits around spinning black holes. I. Exact solution for the Kerr separatrix
,”
Phys. Rev. D
79
,
124013
(
2009
).
10.
R.
Fujita
and
W.
Hikida
, “
Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
,”
Class. Quantum Grav.
26
,
135002
(
2009
).
11.
Z. Kh.
Kurmakaev
, “
Circular orbits in the Kerr metric
,”
Sov. Astron.
18
,
110
111
(
1974
).
12.
D.
Bini
and
R. T.
Jantzen
, “
Circular orbits in Kerr spacetime: Equatorial plane embedding diagrams
,”
Class. Quantum Grav.
17
,
1637
1647
(
2000
).
13.
D.
Pugliese
,
H.
Quevedo
, and
R.
Ruffini
, “
Circular motion of neutral test particles in Reissner-Nordström spacetime
,”
Phys. Rev. D
83
,
024021
(
2011
).
14.
A.
Wünsch
,
T.
Müller
,
D.
Weiskopf
, and
G.
Wunner
, “
Circular orbits in the extreme Reissner-Nordstrøm dihole metric
,”
Phys. Rev. D
87
,
024007
(
2013
).
15.
M.
Visser
,
Lorentzian Wormholes—From Einstein to Hawking
(
Springer
,
New York
,
1996
).
16.
T.
Müller
, “
GeodesicViewer—A tool for exploring geodesics in the theory of relativity
,”
Comput. Phys. Commun.
181
,
413
419
(
2010
).
17.
T.
Müller
and
J.
Frauendiener
, “
Studying null- and time-like geodesics in the classroom
,”
Eur. J. Phys.
32
,
747
759
(
2011
).
18.
T.
Müller
and
F.
Grave
, “
Motion4D—A library for lightrays and timelike geodesics in the theory of relativity
,”
Comput. Phys. Commun.
180
,
2355
2360
(
2009
).
19.
C. W.
Misner
,
K. S.
Thorne
, and
J. A.
Wheeler
,
Gravitation
(
W. H. Freeman
,
New York
,
1973
).
20.
Gnuplot is a portable command-line driven graphing utility, see <http://www.gnuplot.info>.
21.
O.
Fechtig
, “
Physikalische Aspekte und Visualisierung von stationären wurmlöchern
,” diploma thesis (in German),
University of Stuttgart
,
Stuttgart, Germany
, ITP1 (
2004
); <http://itp1.uni-stuttgart.de/publikationen/abschlussarbeiten/fechtig_diplom_2004.pdf>.
22.
GRTensor II is a computer algebra package that was originally developed for Maple V, see <http://grtensor.phy.queensu.ca>.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.