We study the motion of a test particle in a stationary, axially and reflection symmetric spacetime of a central compact object, as affected by interaction with a test radiation field of the same symmetries. Considering the radiation flux with fixed but arbitrary (non-zero) angular momentum, we extend previous results limited to an equatorial motion within a zero-angularmomentum photon flux in the Kerr and Schwarzschild backgrounds. While a unique equilibrium circular orbit exists if the photon flux has zero angular momentum, multiple such orbits appear if the photon angular momentum is sufficiently high.PACS number: 04.20.Cv

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We introduce a new methodology for deriving the conservative dynamics of gravitationally interacting binary systems. Our approach combines, in a novel way, several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, gravitational self-force, and effective one-body. We apply our method to the derivation of the fifth post-Newtonian dynamics. By restricting our results to the third post-Minkowskian level, we give the first independent confirmation of the recent result of Bern et al. [Phys. Rev. Lett. 122, 201603 (2019)]. We also offer checks for future fourth post-Minkowskian calculations. Our technique can, in principle, be extended to higher orders of perturbation theory.Introduction.-The detection of the coalescence of compact binaries by the LIGO-Virgo collaboration [1] demands an ever more accurate knowledge of the gravitational dynamics and radiation of binary systems. We propose here a new methodology for improving the theoretical description of the conservative dynamics of twobody systems in General Relativity. This methodology unifies in a novel way an array of previously developed theoretical tools, and combines it with some new insights. This allows one to reach in an expedient manner new high-order results of direct physical significance. Here, we exemplify the efficiency of our method by applying it to the first (essentially complete) computation of the conservative two-body dynamics (of two non-spinning masses m 1 , m 2 ) at the fifth post-Newtonian (5PN) accuracy, i.e. one order in (v/c) 2 beyond the last post-Newtonian (PN) order at which this dynamics has been heretofore fully derived [2][3][4][5][6][7][8]. [Our 5PN-level result cannot be compared with the recent 5PN-level works [9, 10], because the latter have computed only the small, and non gauge-invariant, subset of "static" contributions to the 5PN Hamiltonian.] As a by product of our calculation, we also compute the 5PN-level contribution to the (gauge-invariant) scattering angle of two bodies considered at the third post-Minkowskian (3PM) approximation. We find a result which is in agreement with the corresponding result recently derived from a two-loop scattering amplitude computation [11,12], thereby providing the first confirmation of the latter result going beyond the 4PN-level checks derived from the gauge-invariant 4PN scattering [13]. The result presented here is only a first application of a general methodology which can be extended to higher PN orders.

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