A method based upon the concept of holonomy of a metric space–time (M,g), in order to identify the presence of conical singularities in M is proposed. The validity and usefulness of this so‐called holonomy method is proven by applying it to a set of four‐dimensional space–times and one three‐dimensional space–time. The holonomy method predictions are confirmed by the comparison with the predictions obtained after coordinate transformations which take the metrics g, to a new basis where the global properties of conical singularities are explicitly seen.

1.
H.
Weyl
,
Ann. Phys. (Leipzig)(4.f.)
59
,
185
(
1917
).
2.
F. J. Tipler, C. J. S. Clarke, and G. F. R. Ellis, in General Relativity and Gravitation—One Hundred Years After the Birth of A. Einstein, Vol. 2, edited by A. Held and P. Bergman (Plenum, New York, 1980), p. 97.
3.
G. F. R.
Ellis
and
B. G.
Schmidt
,
Gen. Rel. Grav.
10
,
989
(
1979
);
C. J. S. Clarke, The Analysis of Spacetime Singularities—Cambridge Lecture Notes in Physics 1 (Cambridge University, Cambridge, 1993).
4.
T. W. B.
Kibble
,
J. Phys. A
9
,
1387
(
1976
).
5.
A.
Vilenkin
,
Phys. Rev. D
23
,
852
(
1981
).
6.
E. P. S. Shellard, in Gravitation: The Spacetime Structure, SILARG VIII, Proceedings of the 8th Latin American Symposium on Relativity and Gravitation, edited by P. S. Letelier and W. A. Rodrigues, Jr. (World Scientific, Singapore, 1994), pp. 3–49.
7.
A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University, Cambridge, 1994).
8.
M.
Aryal
,
L. H.
Ford
, and
A.
Vilenkin
,
Phys. Rev. D
34
,
2263
(
1986
);
A. Vilenkin, in 300 Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge University, Cambridge, 1987), pp. 499–523.
9.
S.
Deser
,
R.
Jackiw
, and
G.
’t Hooft
,
Ann. Phys. (NY)
152
,
220
(
1984
);
R. Jackiw, in Physics, Geometry, and Topology, edited by H. C. Lee (Plenum, New York, 1990), pp. 191–239.
10.
J.
Louko
and
P. J.
Ruback
,
Class. Quantum Grav.
8
,
91
(
1991
).
11.
For an introductory approach see M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics (Adam Hilger, Bristol, 1990), pp. 232–234;
and M. Crampin and F. A. E. Pirani, Applicable Differential Geometry, London Mathematical Society Lecture Note Series 59 (Cambridge University, Cambridge, 1986), p. 378. For a more advanced consideration, see S. Salamon, Riemannian Geometry and Holonomy Groups, Pitman Research Notes in Mathematics Series 201 (Longman Scientific & Technical, New York, 1989).
12.
N. L.
Balazs
and
A.
Voros
,
Phys. Rep.
143
,
109
(
1986
).
13.
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, New York, 1973).
14.
J. A. Wolf, Spaces of Constant Curvature (McGraw-Hill, New York, 1967);
W. P. Thurston, The Geometry and Topology of Three-Spacetimes (Princeton University, Princeton, 1982).
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