The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: Potential contributions

Abstract

Within an effective field theory method to general relativity, we calculate the fifth-order post-Newtonian (5 PN) Hamiltonian dynamics also for the tail terms, extending earlier work on the potential contributions, working in harmonic coordinates. Here we calculate independently all (local) 5 PN contributions to the tail terms using the in-in formalism, on which we give a detailed account. The five expansion terms of the Hamiltonian in the effective one body (EOB) approach, q 82 , q 63 , q 44 , d5 and a 6 , can all be determined from the local contributions to periastron advance K loc,h ( Ê, j), without further assumptions on the structure of the symmetric mass ratio, ν, of the expansion coefficients of the scattering angle χ k . The O(ν 2 ) contributions to the 5 PN EOB parameters have been unknown in part before. We perform comparisons of our analytic results with the literature and also present numerical results on some observables.

Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

“…1 The state of affairs rapidly progressed thereafter, notably after to the development of the effective field theory (EFT) approach in [30,31] (see [32][33][34] for reviews), and spin effects in the PN conservative dynamics are currently known to N 2 LO [27,[35][36][37][38][39][40][41][42][43], and partial results at O(G 4 ) [44,45], with generic orientations; and to N 3 LO [46,47] with aligned-spin configurations. 2 This complements our knowledge of spin-independent conservative contributionsboth from potential and radiation-reaction effects -which are known up to N 5 LO [62][63][64][65][66][67][68][69][70][71][72][73][74][75], with partial results at higher orders computed using various methodologies, e.g. [76][77][78][79].…”

Classical black hole scattering from a worldline quantum field theory

“…The suitably non-relativistically decomposed graviton field h µν (x) is integrated out in the path integral while the worldline trajectories of the black holes x µ i (τ i ) are kept as classical background sources. The state of the art is 4PN level for the potential [22][23][24][25][26][27][28][29][30][31][32], parts of 5PN [33][34][35][36] and 6PN [37][38][39][40][41][42], and 3PN [43][44][45] for the gravitational radiation emitted from a quasi-circular inspiral (see also ref. [46]).…”

SUSY in the sky with gravitons

“…[28,29] for reviews of the PN framework. Impressively high orders in the PN [32][33][34][35][36][37] and PM [38][39][40][41] expansions have also been established.…”