Geometric structures of the classical general relativistic phase space

JANYŠKA, Josef and Marco MODUGNO. Geometric structures of the classical general relativistic phase space. International Journal of Geometrical Methods in Modern Physics. World Scientific, 2008, vol. 5, No 5, p. 699-754. ISSN 0219-8878.

Basic information

• Original name: Geometric structures of the classical general relativistic phase space
• Name in Czech: Geometrické struktury klasického obecně relativistického fázového prostoru
• Authors: JANYŠKA, Josef (203 Czech Republic, guarantor) and Marco MODUGNO (380 Italy).
• Edition: International Journal of Geometrical Methods in Modern Physics, World Scientific, 2008, 0219-8878.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United Kingdom of Great Britain and Northern Ireland
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 1.464
• RIV identification code: RIV/00216224:14310/08:00024916
• Organization unit: Faculty of Science
• UT WoS: 000259928300004
• Keywords in English: Spacetime; phase space; spacetime connection; phase connection; Schouten bracket; Froelicher Nijenhuis bracket; symplectic structure; Poisson structure; Jacobi structure
• Tags: Froelicher Nijenhuis bracket, Jacobi structure, phase connection, phase space, Poisson structure, Schouten bracket, spacetime, spacetime connection, symplectic structure
• Tags: International impact, Reviewed

Abstract

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the geometric conditions by which the Lorentz metric and a connection of the phase space yield contact and Jacobi structures. In particular, we specialise these conditions to the cases when the connection of the phase space is generated by the metric and an additional tensor. Indeed, the case generated by the metric and the electromagnetic field is included, as well.

Abstract (in Czech)

Článek se zabývá geometrickými vlastnostmi fázového prostoru klasické obecně-relativistické částice. Fázový prostor je chápán jako prostor 1-jetů pohybů. Hlavním cílem je určit geometrické struktury, které jsou dány Lorentzovou metrikou a fázovou konexí. Dostáváme tak podmínky pro kontaktní a Jakobiho strukturu.

Links

• GA201/05/0523, research and development project: Name: Geometrické struktury na fibrovaných varietách

Investor: Czech Science Foundation, Geometric structures on fibered manifolds

• MSM0021622409, plan (intention): Name: Matematické struktury a jejich fyzikální aplikace

Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures and their physical applications