Correspondence of Concept of Circular Orbits in Schwarzschild Metric and Kerr Metric to those in Tidally Evolving Binaries in Weak Gravitational Regime and its Application in Determination of Spin of Supermassive Black Hole

Abstract

Bijay Kumar Sharma

This paper rederives diameters of the Innermost Stable Circular Orbits (ISCO) in Schwarzschild Metric (RDISCO = 6RSch for non-rotating BH with a =0) and in Kerr metric with particular reference to recently studied Super Massive Black Hole in NGC1365 (RDISCO = 9RSch for retrograde orbits and RDISCO = 1RSch for prograde orbits around maximally spinning BH of a=1). Next the same derivations are made in tidally evolving binaries based on kinematic model. Kinematic Model derivation corresponds to the derivations made in Kerr Metric for Circular Orbits in all its details at weak gravitation regime. At strong gravitation regime in Kerr metric, the two orbits converge to Innermost Stable Circular Orbit due to the Space-Time Curvature and Frame-Dragging Effect in the vicinity of SMBH. Kinematic model fails to arrive at ISCO since it has not included the relativistic mechanics.

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