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We compute the static contribution to the gravitational interaction potential of two point masses in the velocity-independent five-loop (and 5th post-Newtonian) approximation to the harmonic coordinates effective action in a direct calculation. The computation is performed using effective field methods based on Feynman diagrams in momentum-space in $d = 3 - 2varepsilon$ space dimensions. We also reproduce the previous results including the 4th post-Newtonian order.
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We determine the gravitational interaction between two compact bodies up to the sixth power in Newtons constant GN, in the static limit. This result is achieved within the effective field theory approach to General Relativity, and exploits a manifest factorization property of static diagrams which allows to derive static post Newtonian (PN) contributions of (2n+1)-order in terms of lower order ones. We recompute in this fashion the 1PN and 3PN static potential, and present the novel 5PN contribution.
We discuss the first-time calculation of the static gravitational two-body potential up to fifth post-Newtonian(PN) order. The results are achieved through a manifest factorization property of the odd PN diagrams. The factorization property is illustrated also at first and third PN order.
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We compute the quasi-bound state spectra of ultralight scalar and vector fields around rotating black holes. These spectra are determined by the gravitational fine structure constant $alpha$, which is the ratio of the size of the black hole to the Compton wavelength of the field. When $alpha$ is small, the energy eigenvalues and instability rates can be computed analytically. Since the solutions vary rapidly near the black hole horizon, ordinary perturbative approximations fail and we must use matched asymptotic expansions to determine the spectra. Our analytical treatment relies on the separability of the equations of motion, and is therefore only applicable to the scalar field and the electric modes of the vector field. However, for slowly-rotating black holes, the equations for the magnetic modes can be written in a separable form, which we exploit to derive their energy eigenvalues and conjecture an analytic form for their instability rates. To check our conjecture, and to extend all results to large values of $alpha$, we solve for the spectra numerically. We explain how to accurately and efficiently compute these spectra, without relying on separability. This allows us to obtain reliable results for any $alpha gtrsim 0.001$ and black holes of arbitrary spin. Our results provide an essential input to the phenomenology of boson clouds around black holes, especially when these are part of binary systems.
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