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Passer au global : le cas d’Élie Cartan, 1922–1930

Renaud Chorlay (2009)

Revue d'histoire des mathématiques

Après avoir enrichi la notion de connexion entre 1922 et 1925, Élie Cartan jette entre 1925 et 1930 les bases de l’étude topologique et géométrique globale des groupes de Lie et variétés homogènes. Nous voulons montrer que ce passage aux questions globales s’accompagne d’une réorganisation complète, aux niveaux théorique, thématique et rhétorique, autour d’une polarité local / global jusque là absente des travaux de Cartan ; elle remplace, selon nous, une polarité infinitésimal / fini héritée du...

Polyhomogeneous solutions of wave equations in the radiation regime

Piotr T. Chruściel, Olivier Lengard (2000)

Journées équations aux dérivées partielles

While the physical properties of the gravitational field in the radiation regime are reasonably well understood, several mathematical questions remain unanswered. The question here is that of existence and properties of gravitational fields with asymptotic behavior compatible with existence of gravitational radiation. A framework to study those questions has been proposed by R. Penrose (R. Penrose, “Zero rest-mass fields including gravitation”, Proc. Roy. Soc. London A284 (1965), 159-203), and developed...

Post-Newtonian approximation in the test particle limit

Misao Sasaki (1997)

Banach Center Publications

Gravitational radiation from a small mass particle orbiting a massive black hole can be analytically studied to a very high order in the post-Newtonian expansion. Thus it gives us useful information on the evolution of a coalescing compact binary star. In this talk, I report on recent progress made in the black-hole perturbation approach.

Post-Newtonian approximations and equations of motion of general relativity

Gerhard Schäfer (1997)

Banach Center Publications

A post-Newtonian approximation scheme for general relativity is defined using the Arnowitt-Deser-Misner formalism. The scheme is applied to perfect fluids and point-mass systems. The two-body point-mass Hamiltonian is given explicitly up to the post 2 . 5 -Newtonian order.

Post-Newtonian hydrodynamic equations using the (3+1) formalism in general relativity

Hideki Asada (1997)

Banach Center Publications

The post-Newtonian (PN) hydrodynamic equations are obtained in the (3+1) formalism, which include the 2.5PN order as the reaction due to the quadrupole gravitational radiation. These equations are valid in various slice conditions, while we adopt a kind of transverse gauge condition to determine the shift vector. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. Our formulaton in the PN approximation using the (3+1) formalism will be useful...

Precession of the perihelion within a generalized theory for the two body problem

Franco Cardin (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Sulla base di una teoria generalizzata di Meccanica Classica per il problema dei Due Corpi, recentemente formulata dall'autore, si considera la questione della precessione del perielio dei pianeti, assente nel caso Newtoniano. Si mostra come la descrizione di questo fenomeno in tale teoria generalizzata è sostanzialmente equivalente a quella offerta dalla Relatività Generale.

Principe de recollement des équations des contraintes en relativité générale

Julien Cortier (2011/2012)

Séminaire de théorie spectrale et géométrie

La méthode de «  recollement  » permettant de trouver des solutions des équations des contraintes relativistes est décrite. En particulier, on expose la méthode de Corvino-Schoen pour construire des familles de solutions sur une variété non-compacte avec géométrie prescrite sur un bout asymptotique, en insistant sur le recollement «  non-localisé  ». Une liste de résultats obtenus par divers auteurs à partir de telles techniques est alors fournie, incluant la question du recollement de métriques...

Progress towards a local expression for radiation reaction

Rachel Capon (1997)

Banach Center Publications

We report on progress towards finding a local expression for radiation reaction for a particle orbiting a Kerr black hole. The Dirac-Gal'tsov approach is described. For the case of a scalar particle in a circular orbit of a Schwarzschild black hole, an explicit calculation is done via this method and shown to be in agreement with overall energy conservation. A possible approach to the case of more general orbits is also discussed.

Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures

S. Hronek, R. Suchánek (2022)

Archivum Mathematicum

We study properties of pseudo-Riemannian metrics corresponding to Monge-Ampère structures on four dimensional T * M . We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Plücker embedding equation. We also focus on pullbacks of the pseudo-metrics on two dimensional M , and describe the corresponding Hessian structures.

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