Secular dynamics of binaries in stellar clusters -- III. Doubly-averaged
  dynamics in the presence of general relativistic precession
  Secular evolution of binaries driven by an external (tidal) potential is a
classic astrophysical problem. Tidal perturbations can arise due to an external
point mass, as in the Lidov-Kozai (LK) theory of hierarchical triples, or due
to an extended stellar system (e.g. galaxy or globular cluster) in which the
binary resides. For many applications, general-relativistic (GR) apsidal
precession is important, and has been accounted for in some LK calculations.
Here we generalise and extend these studies by exploring in detail the effect
of GR precession on (quadrupole-level) tidal evolution of binaries orbiting in
arbitrary axisymmetric potentials (which includes LK theory as a special case).
We study the (doubly-averaged) orbital dynamics for arbitrary strengths of GR
and binary initial conditions and uncover entirely new phase space morphologies
with important implications for the binary orbital evolution. We also explore
how GR precession affects secular evolution of binary orbital elements when the
binary reaches high eccentricity ($e\to 1$) and delineate several different
dynamical regimes. Our results are applicable to a variety of astrophysical
systems. In particular, they can be used to understand the high-eccentricity
behaviour of (cluster) tide-driven compact object mergers -- i.e. LIGO/Virgo
gravitational wave sources -- for which GR effects are crucial.
