We discuss the correspondence between spinning, charged spherical sources in electrodynamics and spinning, massive spherical sources in linearized general relativity and show that the form of the potentials and equations of motion are similar in the two cases in the slow motion limit. This similarity allows us to interpret the Kerr metric in analogy with a spinning sphere in electrodynamics and aids in understanding linearized general relativity, where the “forces” are effective and come from the intrinsic curvature of space-time.

1.
Robert M.
Wald
,
General Relativity
(
Univ. of Chicago
,
Chicago
,
1984
).
2.
Ray
D’Inverno
,
Introducing Einstein’s Relativity
(
Oxford U. P.
,
Oxford
,
1992
).
3.
Charles W.
Misner
,
Kip S.
Thorne
, and
John Archibald
Wheeler
,
Gravitation
(
Freeman
,
New York
,
1973
).
4.
David J.
Griffiths
,
Introduction to Electrodynamics
, 3rd ed. (
Prentice Hall
,
Upper Saddle River, NJ
,
1999
).
5.
Herbert
Goldstein
,
Classical Mechanics
, 2nd ed. (
Addison-Wesley
,
Reading, MA
,
1980
).
6.

We have the usual relation, dτdt=1v2c2.

7.
Roy
P.
Kerr
, “
Gravitational field of a spinning mass as an example of algebraically special metrics
,”
Phys. Rev. Lett.
11
(
5
),
237
238
(
1963
).
8.
Robert H.
Boyer
and
Richard W.
Lindquist
, “
Maximal analytic extension of the Kerr metric
,”
J. Math. Phys.
8
(
2
),
265
281
(
1967
).
9.
R. H.
Boyer
and
T. G.
Price
, “
An interpretation of the Kerr metric in general relativity
,”
Proc. Cambridge Philos. Soc.
61
,
265
281
(
1965
).
10.
S.
Chandrasekhar
,
The Mathematical Theory of Black Holes
(
Oxford U. P.
,
Oxford
,
1992
).
11.
S.
Deser
and
J.
Franklin
, “
Time (in)dependence in general relativity
,”
Am. J. Phys.
75
,
281
283
(
2007
).
12.
L. D.
Landau
and
E. M.
Lifshitz
,
The Classical Theory of Fields
(
Butterworth-Heinenann
,
Oxford
,
1996
).
13.
James B.
Hartle
,
Gravity: An Introduction to Einstein’s General Relativity
(
Addison-Wesley
,
San Francisco, CA
,
2003
).
14.
Michael D.
Hartl
, “
Dynamics of spinning test particles in Kerr spacetime
,”
Phys. Rev. D
67
,
024005
1
(
2003
).
15.
A.
Papapetrou
, “
Spinning test-particles in general relativity I
,”
Proc. R. Soc. London
209
,
248
258
(
1951
).
17.
Brandon
Carter
, “
Global structure of the Kerr family of gravitational fields
,”
Phys. Rev.
174
(
3
),
1559
1571
(
1968
).
18.
Fernando
de Felice
and
Giovanni
Preti
, “
On the meaning of the separation constant in the Kerr metric
,”
Class. Quantum Grav.
16
,
2929
2935
(
1999
).
19.
W. G.
Dixon
, “
Dynamics of extended bodies in general relativity. I. Momentum and angular momentum
,”
Proc. R. Soc. London
314
(
1519
),
499
527
(
1970
).
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.