Comparing Criteria for Circular Orbits in General Relativity

Abstract

We study a simple analytic solution to Einstein's field equations describing a thin spherical shell consisting of collisionless particles in circular orbit. We then apply two independent criteria for the identification of circular orbits, which have recently been used in the numerical construction of binary black hole solutions, and find that both yield equivalent results. Our calculation illustrates these two criteria in a particularly transparent framework and provides further evidence that the deviations found in those numerical binary black hole solutions are not caused by the different criteria for circular orbits.

4 pages; to appear in PRD as a Brief Report; added and corrected references

References in corpus (12)

• Effective one-body approach to general relativistic two-body dynamics
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Conformal ``thin sandwich'' data for the initial-value problem of general relativity
• Binary black holes in circular orbits. II. Numerical methods and first results
• Binary black holes in circular orbits. I. A global spacetime approach
• Three-dimensional initial data for the collision of two black holes II: Quasi-circular orbits for equal-mass black holes
• The Innermost Stable Circular Orbit of Binary Black Holes
• Innermost circular orbit of binary black holes at the third post-Newtonian approximation
• Circular orbits of corotating binary black holes: comparison between analytical and numerical results
• Quasi-circular Orbits for Spinning Binary Black Holes
• Comparing initial-data sets for binary black holes
• Gravitational Wavetrains in the Quasi-Equilibrium Approximation: A Model Problem in Scalar Gravitation

Cited by in corpus (8)

• Circular orbits and spin in black-hole initial data
• Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium Formulation
• Gauge conditions for binary black hole puncture data based on an approximate helical Killing vector
• Quasi-equilibrium Binary Black Hole Initial Data for Dynamical Evolutions
• Can a combination of the conformal thin-sandwich and puncture methods yield binary black hole solutions in quasi-equilibrium?
• Conformal-thin-sandwich initial data for a single boosted or spinning black hole puncture
• Measuring eccentricity in binary black-hole initial data
• Shells around black holes: the effect of freely specifiable quantities in Einstein's constraint equations