 
FIZIKA B 13 (2004) 4, 699710
CORRESPONDENCE BETWEEN TEST AND EFFECTIVEPARTICLE EQUATIONS OF MOTION
IN RELATIVISTIC GRAVITATIONAL TWOBODY PROBLEM
S. B. FARUQUE
Department of Physics, Shah Jalal University of Science and Technology, Sylhet 3114,
Bangladesh
Email address: awsbf62@yahoo.com
Received 22 December 2003; Accepted 15 November 2004
Online 2 February 2005
The correspondence between the test and effectiveparticle equations of motion of a
nonrelativistic gravitational twobody system is well understood. But the same is not
true for a relativistic twobody system. This is because the effective onebody approach
to a relativistic twobody problem is not yet fully elucidated. Among the known two
effective onebody approaches to relativistic twobody problem, we follow up the one
addressed through a constraint Hamiltonian. We investigate the correspondence of the
resulting effective onebody equation of motion with the geodetical equation of motion of
a test body in the Schwarzschild field. Next, we extend the twobody problem by endowing a
spin to the central body, and examine again the correspondence between the effective
onebody equations of motion of such a problem with the testbody description. In
particular, we show the relation between the Carter’s equations of geodetical motion in
the Kerr field with the equations indicated by the effective onebody approach of the
twobody problem. In both the Schwarzschild and the Kerr fields, we determine the location
of the innermost stable circular orbit (ISCO), which is an important key for the study of
astrophysical binary stars. Subsequently, we examine the correspondence between the ISCO
in the testparticle orbit and in the effectiveparticle orbit.
PACS numbers: 95.30.Sf
UDC 539.12
Keywords: testparticle, effectiveparticle, twobody problem, relativistic
gravitation
