Original scientific paper

**Correspondence between test- and effective-particle equations of motion in relativistic gravitational two-body problem**

S. B. Faruque
; Department of Physics, Shah Jalal University of Science and Technology, Sylhet 3114, Bangladesh

###### Abstract

The correspondence between the test- and effective-particle equations of motion of a non-relativistic gravitational two-body system is well understood. But the same is not true for a relativistic two-body system. This is because the effective one-body approach to a relativistic two-body problem is not yet fully elucidated. Among the known two effective one-body approaches to relativistic two-body problem, we follow up the one addressed through a constraint Hamiltonian. We investigate the correspondence of the resulting effective one-body equation of motion with the geodetical equation of motion of a test body in the Schwarzschild field. Next, we extend the two-body problem by endowing a spin to the central body, and examine again the correspondence between the effective one-body equations of motion of such a problem with the test-body description. In particular, we show the relation between the Carters equations of geodetical motion in the Kerr field with the equations indicated by the effective one-body approach of the two-body 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 test-particle orbit and in the effective-particle orbit.

###### Keywords

test-particle; effective-particle; two-body problem; relativistic gravitation

###### Hrčak ID:

305657

###### URI

###### Publication date:

7.11.2004.

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