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One of the greatest theoretical challenges in the build-up to the era ofsecond-generation gravitational-wave detectors is the modeling of genericbinary waveforms. We introduce an approximation that has the potential tosignificantly simplify this problem. We show that generic precessing-binaryinspiral waveforms (covering a seven-dimensional space of intrinsic parameters)can be mapped to a two-dimensional space of non-precessing binaries,characterized by the mass ratio and a single effective total spin. The mappingconsists of a time-dependent rotation of the waveforms into thequadrupole-aligned frame, and is extremely accurate (matches $> 0.99$ withparameter biases in the total spin of $\Delta \chi \leq 0.04$), even in thecase of transitional precession. In addition, we demonstrate a simple method toconstruct hybrid post-Newtonian--numerical-relativity precessing-binarywaveforms in the quadrupole-aligned frame, and provide evidence that ourapproximate mapping can be used all the way to the merger. Finally, based onthese results, we outline a general proposal for the construction of genericwaveform models, which will be the focus of future work.

Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals