Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order

The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation of general relativity has been determined previously. However two ambiguity parameters associated with infra-red (IR) divergencies of spatial integrals had to be introduced. These two parameters were fixed by comparison with gravitational self-force (GSF) calculations of the conserved energy and periastron advance for circular orbits in the test-mass limit. In the present paper together with a companion paper, we determine both these ambiguities from first principle, by means of dimensional regularization. Our computation is thus entirely defined within the dimensional regularization scheme, for treating at once the IR and ultra-violet (UV) divergencies. In particular, we obtain crucial contributions coming from the Einstein-Hilbert part of the action and from the non-local tail term in arbitrary dimensions, which resolve the ambiguities.Comment: 25 pages, published versio

Nitrogen isotopic fractionation during abiotic synthesis of organic solid particles

The formation of organic compounds is generally assumed to result from abiotic processes in the Solar System, with the exception of biogenic organics on Earth. Nitrogen-bearing organics are of particular interest, notably for prebiotic perspectives but also for overall comprehension of organic formation in the young solar system and in planetary atmospheres. We have investigated abiotic synthesis of organics upon plasma discharge, with special attention to N isotope fractionation. Organic aerosols were synthesized from N2-CH4 and N2-CO gaseous mixtures using low-pressure plasma discharge experiments, aimed at simulating chemistry occurring in Titan s atmosphere and in the protosolar nebula, respectively. Nitrogen is efficiently incorporated into the synthesized solids, independently of the oxidation degree, of the N2 content of the starting gas mixture, and of the nitrogen speciation in the aerosols. The aerosols are depleted in 15N by 15-25 permil relative to the initial N2 gas, whatever the experimental setup is. Such an isotopic fractionation is attributed to mass-dependent kinetic effect(s). Nitrogen isotope fractionation upon electric discharge cannot account for the large N isotope variations observed among solar system objects and reservoirs. Extreme N isotope signatures in the solar system are more likely the result of self-shielding during N2 photodissociation, exotic effect during photodissociation of N2 and/or low temperature ion-molecule isotope exchange. Kinetic N isotope fractionation may play a significant role in the Titan s atmosphere. We also suggest that the low delta15N values of Archaean organic matter are partly the result of abiotic synthesis of organics that occurred at that time

Conservative Dynamics of Binary Systems of Compact Objects at the Fourth Post-Newtonian Order

We review our recent derivation of a Fokker action describing the conservative dynamics of a compact binary system at the fourth post-Newtonian (4PN) approximation of general relativity. The two bodies are modeled by point particles, which induces ultraviolet (UV) divergences that are cured by means of dimensional regularization combined with a renormalization of the particle's wordlines. Associated with the propagation of wave tails at infinity is the appearance of a non-local-in-time conservative tail effect at the 4PN order in the Lagrangian. In turn this implies the appearance of infrared (IR) divergent integrals which are also regularized by means of dimensional regularization. We compute the Noetherian conserved energy and periastron advance for circular orbits at 4PN order, paying special attention to the treatment of the non-local terms. One ambiguity parameter remaining in the current formalism is determined by comparing those quantities, expressed as functions of the orbital frequency, with self-force results valid in the small mass ratio limit.Comment: 7 pages; contribution to the proceedings of the 52nd Rencontres de Moriond, "Gravitation

La singularité du Pacs

Étude synthétique sur le PacsLa loi du 17 mai 2013 s'inscrit dans la continuité des profondes évolutions que connut le droit des couples en quelques décennies. Désormais chaque individu peut choisir entre trois modes de conjugalité. Au sein de ce pluralisme affirmé, le pacs, introduit en 1999, occupe une place intermédiaire entre l'espace de non-droit que constitue le concubinage, et l'union encore fortement réglementée et ritualisée qu'est le mariage. Cependant, érigé sur le modèle du mariage, le pacs a été sans cesse rapproché de celui-ci par les récentes réformes. La question de sa singularité doit être posée afin que soit préservée l'existence d'un pluralisme équilibré des modes de conjugalité, au cœur duquel il se trouve

Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation

The Fokker action governing the motion of compact binary systems without spins is derived in harmonic coordinates at the fourth post-Newtonian approximation (4PN) of general relativity. Dimensional regularization is used for treating the local ultraviolet (UV) divergences associated with point particles, followed by a renormalization of the poles into a redefinition of the trajectories of the point masses. Effects at the 4PN order associated with wave tails propagating at infinity are included consistently at the level of the action. A finite part procedure based on analytic continuation deals with the infrared (IR) divergencies at spatial infinity, which are shown to be fully consistent with the presence of near-zone tails. Our end result at 4PN order is Lorentz invariant and has the correct self-force limit for the energy of circular orbits. However, we find that it differs from the recently published result derived within the ADM Hamiltonian formulation of general relativity [T. Damour, P. Jaranowski, and G. Sch\"afer, Phys. Rev. D 89, 064058 (2014)]. More work is needed to understand this discrepancy.Comment: 47 pages; references added; Sec. VD enhanced; a few more minor improvement

SS-constrained random matrices

International audienceLet $S$ be a set of $d$-dimensional row vectors with entries in a $q$-ary alphabet. A matrix $M$ with entries in the same $q$-ary alphabet is $S$-constrained if every set of $d$ columns of $M$ contains as a submatrix a copy of the vectors in $S$, up to permutation. For a given set $S$ of $d$-dimensional vectors, we compute the asymptotic probability for a random matrix $M$ to be $S$-constrained, as the numbers of rows and columns both tend to infinity. If $n$ is the number of columns and $m=m_n$ the number of rows, then the threshold is at $m_n= \alpha_d \log (n)$, where $\alpha_d$ only depends on the dimension $d$ of vectors and not on the particular set $S$. Applications to superimposed codes, shattering classes of functions, and Sidon families of sets are proposed. For $d=2$, an explicit construction of a $S$-constrained matrix is given