Analytic toy-model for the ISCO shift

Abstract

A simple black-hole-ring system is proposed as a toy model for the two-body problem in general relativity. This toy-model yields the fractional shift $\Delta {\Omega }_{\text{isco}}/{\Omega }_{\text{isco}}=\frac{29}{81\sqrt{2}}\eta$ in the Schwarzschild ISCO (innermost stable circular orbit) frequency, where $\eta \equiv m/M_{\text{ir}}\ll 1$ is the dimensionless ratio between the mass of the particle and the irreducible mass of the black hole. Our model suggests that the second-order spin-orbit interaction between the black hole and the orbiting particle (the dragging of inertial frames) is the main element determining the observed value of the ISCO shift.

8 pages

References in corpus (4)

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• Spinning Particle Dynamics and ISCO in Covariant Loop Quantum Gravity
• Internal structures and circular orbits for test particles
• Dragging of inertial frames in the composed black-hole-ring system
• The gravitational two-body problem in the vicinity of the light ring: Insights from the black-hole-ring toy model
• Collision of particles near charged MSW black hole in 2 + 1 dimensions
• Marginally bound circular orbits in the composed black-hole-ring system