Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.
Post-Newtonian and Numerical Calculations of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
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abstract
The problem of a compact binary system whose components move on circular orbits is addressed using two different approximation techniques in general relativity. The post-Newtonian (PN) approximation involves an expansion in powers of v/c<<1, and is most appropriate for small orbital velocities v. The perturbative self-force (SF) analysis requires an extreme mass ratio m1/m2<<1 for the components of the binary. A particular coordinate-invariant observable is determined as a function of the orbital frequency of the system using these two different approximations. The post-Newtonian calculation is pushed up to the third post-Newtonian (3PN) order. It involves the metric generated by two point particles and evaluated at the location of one of the particles. We regularize the divergent self-field of the particle by means of dimensional regularization. We show that the poles proportional to 1/(d-3) appearing in dimensional regularization at the 3PN order cancel out from the final gauge invariant observable. The 3PN analytical result, through first order in the mass ratio, and the numerical SF calculation are found to agree well. The consistency of this cross cultural comparison confirms the soundness of both approximations in describing compact binary systems. In particular, it provides an independent test of the very different regularization procedures invoked in the two approximation schemes.
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gr-qc 2years
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Self-force calculations of radiated gravitational wave energy from hyperbolic orbits around Schwarzschild black holes agree with post-Minkowskian results for large impact parameters and velocities up to 0.7c, with further comparisons to post-Newtonian and numerical relativity.
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Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order
Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.
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Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
Self-force calculations of radiated gravitational wave energy from hyperbolic orbits around Schwarzschild black holes agree with post-Minkowskian results for large impact parameters and velocities up to 0.7c, with further comparisons to post-Newtonian and numerical relativity.