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arXiv · 0902.0573

Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole

Leor Barack·Norichika Sago
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Abstract

The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass $M$ has (areal) radius $r_{\rm isco}= 6M G/c^2$. If the particle is endowed with mass $μ(\ll M)$, it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts $Δr_{\rm isco}$ and $ΔΩ_{\rm isco}$ in the ISCO's radius and frequency, at leading order in the mass ratio $μ/M$. We obtain, in the Lorenz gauge, $Δr_{\rm isco}=-3.269 (\pm 0.003)μG/c^2$ and $ΔΩ_{\rm isco}/Ω_{\rm isco}=0.4870 (\pm 0.0006) μ/M$. We discuss the implications of our result within the context of the extreme-mass-ratio binary inspiral problem.

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Leor Barack, Norichika Sago. 2009-04-22. Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole. https://doi.org/10.1103/physrevlett.102.191101

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