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Related papers: Extending the rigidity of general relativity

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Building on works of Boulanger and Goto, we show that Goto's scalar curvature is the moment map for an action of generalized Hamiltonian automorphisms of the associated Courant algebroid, constrained by the choice of an adapted volume form.…

Differential Geometry · Mathematics 2026-02-03 Vestislav Apostolov , Jeffrey Streets , Yury Ustinovskiy

We study a general relativistic particle action obtained by incorporating the Hamiltonian constraints into the formalism as a toy model for general relativity and string theory. We show how a non-vanishing cosmological constant and a…

High Energy Physics - Theory · Physics 2007-05-23 W. F. Chagas-Filho

Following our previous work, a complete classical solution of the CGHS model in Hamiltonian formulation in new variables is given. We preform a series of analyses and transformations to get to the CGHS Hamiltonian in new variables from a…

General Relativity and Quantum Cosmology · Physics 2013-05-24 Saeed Rastgoo

Dynamics generated from Hamiltonians enjoy potential pathways to quantisation, but standard Hamiltonians are only capable of generating conservative forces. Classes of Hamiltonians have been proposed in Berry et al. capable of generating…

Mathematical Physics · Physics 2024-06-28 Fredy Yip , A. C. H. Cheung

We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…

Mathematical Physics · Physics 2025-11-25 Francçois Gay-Balmaz

Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…

Mathematical Physics · Physics 2023-05-01 William Barham , Philip J. Morrison , Eric Sonnendrücker

We consider the most general class of teleparallel gravitational {}{}theories quadratic in the torsion tensor, in three space-time dimensions, and carry out a detailed investigation of its Hamiltonian formulation in Schwinger's time gauge.…

General Relativity and Quantum Cosmology · Physics 2009-10-31 A. A. Sousa , J. W. Maluf

In the Hamiltonian formulation of general relativity, Einstein's equation is replaced by a set of four constraints. Classically, the constraints can be identified with the generators of the hypersurface-deformation Lie algebroid (HDA) that…

High Energy Physics - Theory · Physics 2018-08-08 Martin Bojowald , Suddhasattwa Brahma , Umut Buyukcam , Michele Ronco

This is a continuation of the series of notes on the dynamics of quadratic polynomials. We show the following Rigidity Theorem: Any combinatorial class contains at most one quadratic polynomial satisfying the secondary limbs condition with…

Dynamical Systems · Mathematics 2016-09-06 Mikhail Lyubich

Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution…

General Relativity and Quantum Cosmology · Physics 2013-05-30 Rodolfo Gambini , Jorge Pullin

The general uncertainty principle applied to gravity can be implemented as a set of modified Poisson brackets in the canonical formalism. As such, the theory is not canonical and the resulting equations of motion do not lead to a covariant…

General Relativity and Quantum Cosmology · Physics 2026-05-08 Douglas M. Gingrich

In complex general relativity, Lorentzian space-time is replaced by a four-complex-dimensional complex-Riemannian manifold, with holomorphic connection and holomorphic curvature tensor. A multisymplectic analysis shows that the Hamiltonian…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Giampiero Esposito

In this work, a method for solving the constraints of general relativity is presented, where first all geometrical objects are written in terms of a set of orthonormal triads and a flat Weitzenbock connection, which depends on the triads…

General Relativity and Quantum Cosmology · Physics 2017-07-18 Daniel W. F. Alves

A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…

Mathematical Physics · Physics 2014-09-09 Steven Duplij

We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of…

High Energy Physics - Theory · Physics 2015-05-30 J. Kluson

We discuss a version of Hamiltonian (2+1)-dimensional dynamics, in which one allows nonvanishing Poisson brackets also between the coordinates, and between the momenta. The resulting equations of motion are not any more derivable from a…

High Energy Physics - Theory · Physics 2007-05-23 Ciprian Acatrinei

We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…

High Energy Physics - Theory · Physics 2009-10-31 Hael Collins , Bob Holdom

A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…

General Relativity and Quantum Cosmology · Physics 2007-05-23 C. Bona , T. Ledvinka , C. Palenzuela , M. Zacek

Gauge theories with general covariance are particularly reluctant to quantization. We discuss the example of the Hamiltonian formulation of the relativistic point particle that, despite its apparent simplicity, is of crucial importance…

High Energy Physics - Theory · Physics 2020-01-08 Benjamin Koch , Enrique Muñoz

We find a first--order partial differential equation whose solutions are all ultralocal scalar combinations of gravitational constraints with Abelian Poisson brackets between themselves. This is a generalisation of the Kucha\v{r} idea of…

General Relativity and Quantum Cosmology · Physics 2009-10-28 F. G. Markopoulou