THE LAGRANGIAN APPROACH TO CONSERVED QUANTITIES IN GENERAL RELATIVITY

1991 ◽  
pp. 451-488 ◽  
Author(s):  
Marco FERRARIS ◽  
Mauro FRANCAVIGLIA
Keyword(s):  
General Relativity ◽  
Lagrangian Approach ◽  
Conserved Quantities

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

scholarly journals COLLECTIVE AND RELATIVE VARIABLES FOR A CLASSICAL KLEIN–GORDON FIELD

1999 ◽  
Vol 14 (21) ◽  
pp. 3387-3420 ◽  
Author(s):  
G. LONGHI ◽  
M. MATERASSI
Keyword(s):  
General Relativity ◽  
Asymptotic Behavior ◽  
Harmonic Analysis ◽  
Momentum Space ◽  
Conserved Quantities ◽  
Canonical Transformations ◽  
Collective Variables ◽  
Klein Gordon ◽  
Definition Of

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.9

Gravitational waves in general relativity IX. Conserved quantities

1966 ◽  
Vol 294 (1436) ◽  
pp. 112-122 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Source Distribution ◽  
Conserved Quantities ◽  
Direct Solution ◽  
Multipole Moments ◽  
Einstein Field Equations ◽  
Field Equations

This paper shows how the ten conserved quantities, recently discovered by E. T. Newman and R. Penrose by essentially geometrical techniques, arise in a direct solution of the Einstein field equations. For static fields it is shown that five of the conserved quantities vanish while the remaining five are expressed in terms of the multipole moments of the source distribution.

Conserved quantities of spinning test particles in general relativity. I

1981 ◽  
Vol 375 (1761) ◽  
pp. 185-193 ◽  
Keyword(s):  
General Relativity ◽  
Vector Field ◽  
Tensor Field ◽  
General Scheme ◽  
Killing Vector ◽  
Conserved Quantity ◽  
General Linear ◽  
Killing Vector Field ◽  
Conserved Quantities ◽  
Test Particles

This is the first of two papers devoted to conserved quantities of spinning test particles in general relativity. In this paper, a general scheme is described according to which these quantities can be investigated. It is shown that the general linear conserved quantity consists of a sum, the first term of which is the well known expression constructed from a Killing vector field, and the second term is of the form U kl S kl , where U* ab is a Killing-Yano tensor field, which is constrained by two additional equations.

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