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.

Algebraic Programming in the Hamiltonian Treatment of the Einstein–Maxwell Equations

1998 ◽  
Vol 09 (01) ◽  
pp. 103-111
Author(s):  
Dumitru N. Vulcanov
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Hamiltonian Formulation ◽  
Space Time ◽  
Algebraic Programming ◽  
Constraint Equations ◽  
Free Electromagnetic Field ◽  
New Procedures ◽  
Ibm Pc

We present new procedures in REDUCE language using the EXCALC package (adapted for IBM-PC machines) for algebraic programming in the hamiltonian formulation of Einstein–Maxwell equations. The dynamic and the constraint equations containing specific terms of the interaction of gravity with source-free electromagnetic field are translated into computer procedures. The results obtained by processing some examples of space-time models are presented.

ALGEBRAIC PROGRAMMING IN THE HAMILTONIAN TREATMENT OF AN INFLATIONARY MODEL

1995 ◽  
Vol 06 (03) ◽  
pp. 317-326 ◽  
Author(s):  
DUMITRU N. VULCANOV
Keyword(s):  
Scalar Field ◽  
Hamiltonian Formulation ◽  
Space Time ◽  
Dynamic Equations ◽  
Inflationary Model ◽  
Action Functional ◽  
Algebraic Programming ◽  
Initial Space ◽  
New Procedures ◽  
Inflationary Models

This article presents new procedures in REDUCE language using the EXCALC package (adapted for IBM-PC machines) for algebraic programming in the Hamiltonian formulation of inflationary models based on a scalar field non-minimally coupled with gravity. The (3+1)-dimensional split of the action functional of the model and the constraint and dynamic equations are obtained. These equations are transposed in computer procedures. The results obtained after processing some examples of initial space-time models are presented here.

New Routines for Algebraic Programming of the Dirac Equation

1997 ◽  
Vol 08 (02) ◽  
pp. 273-286 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Dumitru N. Vulcanov
Keyword(s):  
Dirac Equation ◽  
Main Part ◽  
Space Time ◽  
Curved Space ◽  
Algebraic Programming ◽  
Matrix Algebras ◽  
Dirac Matrix ◽  
New Procedures

We present new procedures in the REDUCE language for algebraic programming of the Dirac equation on curved space-time. The main part of the program is a package of routines defining the Pauli and Dirac matrix algebras. Then the Dirac equation is obtained using the facilities of the EXCALC package. Finally we present some results obtained after running our procedures for the Dirac equation on several curved space-times.

On the symplectic formalism for general relativity

1992 ◽  
Vol 436 (1896) ◽  
pp. 141-153 ◽  
Keyword(s):  
General Relativity ◽  
Hamiltonian Formulation ◽  
Solution Space ◽  
Space Time ◽  
Covariant Formalism ◽  
Present Formalism ◽  
Arbitrary Dimensions ◽  
Torsion Free ◽  
Soldering Form

A covariant formalism for the hamiltonian formulation of general relativity in arbitrary dimensions is presented. Specifically, a presymplectic form on the solution space for the vacuum equations in n dimensions is given. The basic variables are taken to be a soldering form and a torsion-free connection on an SO ( p , q )-bundle over the space-time manifold M . It is shown how the present formalism is related to the standard ADM-formalism.

General Relativity

2019 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Hamiltonian Formulation ◽  
Experimental Tests ◽  
High Energy ◽  
Gravitational Energy ◽  
Field Equations ◽  
Physics First ◽  
Condensed Matter Theory ◽  
Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

scholarly journals WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

2011 ◽  
Vol 03 ◽  
pp. 87-97 ◽  
Author(s):  
F. P. POULIS ◽  
J. M. SALIM
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Riemannian Geometry ◽  
Axiomatic Approach ◽  
Space Time ◽  
Weyl Geometry ◽  
Test Particles ◽  
Variational Formalism ◽  
Physical Fields

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

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 Space time geometry in the atomic hydrogenoid system. Approach to a dust relativistic model from causal quantum mechanics

2018 ◽  
Vol 64 (1) ◽  
pp. 18
Author(s):  
G. Gómez ◽  
I. Kotsireas ◽  
I. Gkigkitzis ◽  
I. Haranas ◽  
M.J. Fullana
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
General Equation ◽  
System Approach ◽  
Space Time ◽  
Relativistic Model ◽  
Time Deformation ◽  
Non Local ◽  
De Broglie Bohm

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

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