BN6  PostNewtonian and Analytic Approximations 
Speaker 
Shah, Abhay 
Coauthors 

Talk Title 
Overlap between black hole pertrurbation theory and postNewtonian formalism 
Abstract 
Over the past few decades, various approaches have been developed to model relativistic binary systems. In the postNewtonian 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 selfforce formalism, first and second order in massratio correction to the background geodesic are studied and this makes the theory valid in the regime where the massratio of the two objects is extreme (for any separation distance). In this talk, we will discuss a novel method of calculating postNewtonian parameters that govern extrememassratio quasicircular binary system. Using black hole perturbation theory and arbitraryprecision computer algebra, we obtain very high order postNewtonian 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 postNewtonian expansion. These parameters can then be used to calibrate a relatively new approach of modeling binaries, the effectiveonebody formalism, which generalizes the Newtonian reduced mass problem. 
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