Algebraic programming of Hamiltonian formalism in general relativity: Application to inhomogeneous space-times

1983 ◽  
Vol 15 (3) ◽  
pp. 209-226 ◽  
Author(s):  
A. Moussiaux ◽  
P. Tombal ◽  
J. Demaret
Keyword(s):  
General Relativity ◽  
Hamiltonian Formalism ◽  
Algebraic Programming

Using algebraic programming to teach general relativity

2001 ◽  
Vol 3 (2) ◽  
pp. 65-70 ◽  
Author(s):  
F.A. Ghergu ◽  
D.N. Vulcanov
Keyword(s):  
General Relativity ◽  
Algebraic Programming

scholarly journals Using Algebraic Computing To Teach General Relativity And Cosmology

2012 ◽  
Vol 56 (1) ◽  
pp. 139-144
Author(s):  
Dumitru N. Vulcanov ◽  
Remus-Ştefan Ş. Boată
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Undergraduate Students ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Einstein Equations ◽  
Algebraic Programming ◽  
Algebraic Computing

AbstractThe article presents some new aspects and experience on the use of computer in teaching general relativity and cosmology for undergraduate students (and not only) with some experience in computer manipulation. Some years ago certain results were reported [1] using old fashioned computer algebra platforms but the growing popularity of graphical platforms as Maple and Mathematica forced us to adapt and reconsider our methods and programs. We will describe some simple algebraic programming procedures (in Maple with GrTensorII package) for obtaining and the study of some exact solutions of the Einstein equations in order to convince a dedicated student in general relativity about the utility of a computer algebra system.

scholarly journals Classification of primary constraints for new general relativity in the premetric approach

2021 ◽  
pp. 2140003
Author(s):  
María-José Guzmán ◽  
Shymaa Khaled Ibraheem
Keyword(s):  
General Relativity ◽  
Hessian Matrix ◽  
Hamiltonian Formalism ◽  
Temporal Part ◽  
Tetrad Field ◽  
Mathematical Properties ◽  
Constitutive Tensor ◽  
Hamiltonian Analysis

We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients [Formula: see text] appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients [Formula: see text]. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018).

Hamiltonian formalism for perfect fluids in general relativity

1980 ◽  
Vol 21 (10) ◽  
pp. 2785-2793 ◽  
Author(s):  
Jacques Demaret ◽  
Vincent Moncrief
Keyword(s):  
General Relativity ◽  
Hamiltonian Formalism ◽  
Perfect Fluids

scholarly journals Hamiltonian formalism and constraint analysis of three-form matter models coupled with general relativity

2018 ◽  
Vol 97 (12) ◽  
Author(s):  
David Brizuela ◽  
Iñaki Garay
Keyword(s):  
General Relativity ◽  
Hamiltonian Formalism ◽  
Constraint Analysis

scholarly journals Spinning bodies in general relativity

2016 ◽  
Vol 13 (08) ◽  
pp. 1640002 ◽  
Author(s):  
J. W. van Holten
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Momentum Tensor ◽  
Curved Space ◽  
Constants Of Motion ◽  
Spinning Bodies ◽  
Compact Spinning ◽  
Independent Derivation

A covariant Hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of Hamiltonians accounting for specific properties and interactions of spinning bodies. The dynamics for a minimal and a specific non-minimal Hamiltonian is discussed. An independent derivation of the equations of motion from an appropriate energy–momentum tensor is provided. It is shown how to derive constants of motion, both background-independent and background-dependent ones.

scholarly journals On the nonperturbative graviton propagator

2018 ◽  
Vol 33 (36) ◽  
pp. 1850220 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Functional Integration ◽  
Hamiltonian Formalism ◽  
Planck Scale ◽  
Functional Integral ◽  
Perturbative Expansion ◽  
Length Scale ◽  
Leading Order ◽  
Starting Point ◽  
Graviton Propagator

To reduce general relativity to the canonical Hamiltonian formalism and construct the path (functional) integral in a simpler and, especially in the discrete case, less singular way, one extends the configuration superspace, as in the connection representation. Then we perform functional integration over connection. The module of the result of this integration arises in the leading order of the expansion over a scale of the discrete lapse-shift functions and has maxima at finite (Planck scale) areas/lengths and rapidly decreases at large areas/lengths, as we have mainly considered previously; the phase arises in the leading order (Regge action) of the stationary phase expansion. Now we consider the possibility of confining ourselves to these leading terms in a certain region of the parameters of the theory; consider background edge lengths as an optimal starting point for the perturbative expansion of the theory; estimate the background length scale and consider the form of the graviton propagator. In parallel with the general simplicial structure, we consider the simplest periodic simplicial structure with a part of the variables frozen (“hypercubic”), for which also the propagator in the leading approximation over metric variations can be written in a closed form.

ADM FORMALISM APPLIED TO SOME SPACE-TIME MODELS USING EXCALC ALGEBRAIC PROGRAMMING

1994 ◽  
Vol 05 (06) ◽  
pp. 973-985 ◽  
Author(s):  
DUMITRU N. VULCANOV
Keyword(s):  
General Relativity ◽  
Hamiltonian Formulation ◽  
Space Time ◽  
Algebraic Programming ◽  
Constraint Equations ◽  
New Procedures ◽  
Dynamic Variables ◽  
Ibm Pc

This article presents the results obtained with new procedures in REDUCE language using EXCALC package (adapted for IBM-PC machines) for algebraic programming in the Hamiltonian formulation of general relativity (ADM formalism). The procedures calculate the dynamic and the constraint equations and, in addition, we have extended the obtained procedures in order to perform a complete ADM reductional procedure: solving the constraint equations, changing of variables, reduction of dynamic variables, etc. The results obtained after processing some examples of space-time models are presented here.

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