Monica Skoge
Comparing Criteria for Circular Orbits in General Relativity
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.
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