Conservative self-force correction to the innermost stable circular orbit: Comparison with multiple post-Newtonian-based methods

Abstract

Barack and Sago [Phys. Rev. Lett. 102, 191101 (2009)] have recently computed the shift of the innermost stable circular orbit (ISCO) of the Schwarzschild spacetime due to the conservative self-force that arises from the finite-mass of an orbiting test-particle. This calculation of the ISCO shift is one of the first concrete results of the self-force program, and provides an exact (fully relativistic) point of comparison with approximate post-Newtonian (PN) computations of the ISCO. Here this exact ISCO shift is compared with nearly all known PN-based methods. These include both ''nonresummed'' and ''resummed'' approaches (the latter reproduce the test-particle limit by construction). The best agreement with the exact (Barack-Sago) result is found when the pseudo-4PN coefficient of the effective-one-body (EOB) metric is fit to numerical relativity simulations. However, if one considers uncalibrated methods based only on the currently known 3PN-order conservative dynamics, the best agreement is found from the gauge-invariant ISCO condition of Blanchet and Iyer [Classical Quantum Gravity 20, 755 (2003)], which relies only on the (nonresummed) 3PN equations of motion. This method reproduces the exact testparticle limit without any resummation. A comparison of PN methods with the ISCO in the equal-mass case (computed via sequences of numerical relativity initial-data sets) is also performed. Here a (different) nonresummed method also performs very well (as was previously shown). These results suggest that the EOB approach-while exactly incorporating the conservative test-particle dynamics and having several other important advantages-does not (in the absence of calibration) incorporate conservative self-force effects more accurately than standard PN methods. I also consider how the conservative self-force ISCO shift, combined in some cases with numerical relativity computations of the ISCO, can be used to constrain our knowledge of (1) the EOB effective metric, (2) phenomenological inspiral-merger-ringdown templates, and (3) 4PN-and 5PN-order terms in the PN orbital energy. These constraints could help in constructing better gravitational-wave templates. Lastly, I suggest a new method to calibrate unknown PN terms in inspiral templates using numerical-relativity calculations.

Comparison between self-force and post-Newtonian dynamics: Beyond circular orbits

“…These results led to a plethora of comparisons between PN, GSF and numerical relativity [25][26][27][28][29][30] and the subsequent refinement of EOB theory [31][32][33][34]. More recently, the geodetic spin precession along circular orbits was computed by Dolan et al through linear order in the mass ratio, and the numerical results successfully compared to a 3PN-accurate prediction [35].…”

Tidal invariants for compact binaries on quasicircular orbits

“…This comparison was shortly followed by calculations of the conservative shift at OðμÞ in the innermost stable circular orbit (ISCO) [14], and the periastron advance of eccentric orbits [15]. This strand of work led to comparisons of PN, GSF and NR data [16][17][18][19][20], and the refinement of EOB models [21][22][23][24].…”

Self-gravitating ring of matter in orbit around a black hole: the innermost stable circular orbit

“…This characteristic frequency is often regarded as the end-point of the in-spiral gravitational tema e-mail: shaharhod@gmail.com plates [5]. For a test particle in the Schwarzschild-black-hole spacetime, this frequency is given by the well-known relation [1][2][3][4][5][6][7][8][9][10][11] …”

“…In particular, the ISCO separates stable circular orbits from orbits that plunge into the central black hole [2]. This special geodesic therefore plays a central role in the two-body dynamics of in-spiralling compact binaries since it marks the critical point where the character of the motion sharply changes [5]. In addition, this marginally stable orbit is usually regarded as the inner edge of accretion disks in composed black-hole-disk systems [2].…”

“…The geodesic motions of test particles in black-hole spacetimes are an important source of information on the structure of the spacetime geometry [1][2][3][4][5][6][7][8][9][10][11]. Of particular importance is the innermost stable circular orbit (ISCO).…”