Griffiths variational multisymplectic formulation for Lovelock gravity

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Aug 2020Embargo end date: 01 Jan 2019 English Publisher:Springer Science and Business Media LLCJournal:General Relativity and Gravitation, volume 52 (issn: 0001-7701, eissn: 1572-9532,

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Authors: Capriotti, Santiago; Gaset Rifà, Jordi; Román Roy, Narciso; Salomone, Leandro;

doi: 10.1007/s10714-020-02725-8 , 10.48550/arxiv.1911.07278

arXiv: 1911.07278

handle: 2117/334744 , 11336/135198

Griffiths variational multisymplectic formulation for Lovelock gravity

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Abstract

This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational problem for the Lovelock Lagrangian, obtaining the geometric form of the corresponding field equations. We give the unified Lagrangian--Hamiltonian formulation of this model and we study the correspondence between the unified formulations for the Einstein--Hilbert and the Einstein--Palatini models of gravity.

37 pp. Some shorts comments are added. Minor corrections. The bibliography is updated and a reference has been added

Related Organizations

Universitat Politècnica de Catalunya
Spain
National Scientific and Technical Research Council
Argentina
Universidad Nacional del Sur
Argentina
Universitat Polite`cnica de Catalunya
Spain
Autonomous University of Barcelona
Spain

Keywords

Einstein equations, High Energy Physics - Theory, optimization::49S05 Variational principles of physics, Camps, Optimització matemàtica, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], FIELD THEORY, General Relativity and Quantum Cosmology, jet bundles, EINSTEIN EQUATIONS, GRIFFITHS VARIATIONAL PROBLEM, https://purl.org/becyt/ford/1.1, including asymmetric field theories, Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories, Mathematical Physics, Mathematical optimization, Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització, PDEs in connection with relativity and gravitational theory, Mathematical Physics (math-ph), Relativistic gravitational theories other than Einstein's, including asymmetric field theories, :49 Calculus of variations and optimal control [Classificació AMS], Classificació AMS::49 Calculus of variations and optimal control, Variational principles of physics, Field theory (Physics), Classificació AMS::83 Relativity and gravitational theory::83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories, JET BUNDLES, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), field theory, Lagrangian and Hamiltonian formalisms, Classificació AMS::49 Calculus of variations and optimal control; optimization::49S05 Variational principles of physics, :49S05 Variational principles of physics [optimization], Field theory · Lagrangian and Hamiltonian formalisms · Jet bundles · Multisymplectic manifolds · Griffiths variational problem · Lovelock gravity · Hilbert–Einstein and Einstein–Palatini actions · Einstein equations, :83 Relativity and gravitational theory::83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories [Classificació AMS], Classificació AMS::83 Relativity and gravitational theory::83D05 Relativistic gravitational theories other than Einstein's, :70 Mechanics of particles and systems::70S Classical field theories [Classificació AMS], Griffiths variational problem, Lovelock gravity, Camps, Teoria dels (Física), https://purl.org/becyt/ford/1, LOVELOCK GRAVITY, Primary: 49S05, 70S05, 83D05, Secondary: 35Q75, 35Q76, 53D42, 55R10, HILBERT–EINSTEIN AND EINSTEIN–PALATINI ACTIONS, :Física [Àrees temàtiques de la UPC], Symplectic field theory; contact homology, Àrees temàtiques de la UPC::Física, Relativity (Physics), Fiber bundles in algebraic topology, Relativitat (Física), Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems, multisymplectic manifolds, High Energy Physics - Theory (hep-th), Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Teoria dels (Física), MULTISYMPLECTIC MANIFOLDS, Hilbert-Einstein and Einstein-Palatini actions, LAGRANGIAN AND HAMILTONIAN FORMALISMS, :Matemàtiques i estadística::Investigació operativa::Optimització [Àrees temàtiques de la UPC]

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