Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force

摘要

The innermost stable circular orbit (ISCO) delimits the transition fromcircular orbits to those that plunge into a black hole. In the test-mass limit,well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes.In the finite-mass case, there are a large variety of ways to define an ISCO ina post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCOcondition of Blanchet & Iyer (2003) to the case of spinning (nonprecessing)binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpectedproperties: (1) it exactly reproduces the Schwarzschild ISCO in the test-masslimit, and (2) it accurately approximates the recently-calculated shift in theSchwarzschild ISCO frequency due to the conservative-piece of the gravitationalself-force [Barack & Sago (2009)]. The generalization of this ISCO condition tospinning binaries has the property that it also exactly reproduces the KerrISCO in the test-mass limit (up to the order at which PN spin corrections arecurrently known). The shift in the ISCO due to the spin of the test-particle isalso calculated. Remarkably, the gauge-invariant PN ISCO condition exactlyreproduces the ISCO shift predicted by the Papapetrou equations for afully-relativistic spinning particle. It is surprising that an analysis of thestability of the standard PN equations of motion is able (without any form of"resummation") to accurately describe strong-field effects of the Kerrspacetime. The ISCO frequency shift due to the conservative self-force in Kerris also calculated from this new ISCO condition, as well as from theeffective-one-body Hamiltonian of Barausse & Buonanno (2010). These resultsserve as a useful point-of-comparison for future gravitational self-forcecalculations in the Kerr spacetime.