BN6 - Post-Newtonian and Analytic Approximations |
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Speaker |
Shah, Abhay |
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| Talk Title |
Overlap between black hole pertrurbation theory and post-Newtonian formalism |
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Abstract |
Over the past few decades, various approaches have been developed to model relativistic binary systems. In the post-Newtonian framework, relativistic corrections, in v/c, are added to the Newtonian problem which makes it valid in the regime where the separation distance between the objects (of any mass ratio) is very large. In black hole perturbation theory or the self-force formalism, first and second order in mass-ratio correction to the background geodesic are studied and this makes the theory valid in the regime where the mass-ratio of the two objects is extreme (for any separation distance). In this talk, we will discuss a novel method of calculating post-Newtonian parameters that govern extreme-mass-ratio quasi-circular binary system. Using black hole perturbation theory and arbitrary-precision computer algebra, we obtain very high order post-Newtonian expansion of invariants that govern the binary. By writing solutions of equations describing the gravitational field in terms of known analytical functions, we calculate these invariants with an accuracy of about 1 part in 10^{500} and study their post-Newtonian expansion. These parameters can then be used to calibrate a relatively new approach of modeling binaries, the effective-one-body formalism, which generalizes the Newtonian reduced mass problem. |
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