A Study of Elliptical Last Stable Orbits About a Massive Kerr Black Hole

Abstract

The last stable orbit (LSO) of a compact object (CO) is an important boundary condition when performing numerical analysis of orbit evolution. Although the LSO is already well understood for the case where a test-particle is in an elliptical orbit around a Schwarzschild black hole (SBH) and for the case of a circular orbit about a Kerr black hole (KBH) of normalised spin, S (|J|/M^2, where J is the spin angular momentum of the KBH); it is worthwhile to extend our knowledge to include elliptical orbits about a KBH. This extension helps to lay the foundation for a better understanding of gravitational wave (GW) emission. The mathematical developments described in this work sprang from the use of an effective potential (V) derived from the Kerr metric, which encapsulates the Lense-Thirring precession. That allowed us to develop a new form of analytical expression to calculate the LSO Radius for circular orbits (R_LSO) of arbitrary KBH spin. We were then able to construct a numerical method to calculate the latus rectum (l_LSO) for an elliptical LSO. Abstract Formulae for E^2 (square of normalised orbital energy) and L^2 (square of normalised orbital angular momentum) in terms of eccentricity, e, and latus rectum, l, were previously developed by others for elliptical orbits around an SBH and then extended to the KBH case; we used these results to generalise our analytical l_LSO equations to elliptical orbits. LSO data calculated from our analytical equations and numerical procedures, and those previously published, are then compared and found to be in excellent agreement.

42 pages, 9 figures, accepted for publication in Classical and Quantum Gravity

References in corpus (3)

• Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
• An investigation of uniform expansions of large order Bessel functions in Gravitational Wave Signals from Pulsars
• The transition from adiabatic inspiral to geodesic plunge for a compact object around a massive Kerr black hole: Generic orbits

Cited by in corpus (4)

• Post-Circular Expansion of Eccentric Binary Inspirals: Fourier-Domain Waveforms in the Stationary Phase Approximation
• Equatorial circular motion in Kerr spacetime
• A Fourier Domain Waveform for Non-Spinning Binaries with Arbitrary Eccentricity
• The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole: I. circular orbits