Journal of Nonlinear Mathematical Physics

Volume 17, Issue 1, March 2010, Pages 13 - 25

Approximate Partial Noether Operators of the Schwarzschild Spacetime

Authors
Ibrar Hussain*, , F. M. Mahomed, §, Asghar Qadir*,
*Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of the College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South Africa
Corresponding Author
Ibrar Hussain
Received 13 July 2008, Accepted 11 June 2009, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925110000556How to use a DOI?
Keywords
Approximate partial Noether operators, Schwarzschild spacetime, perturbed Lagrangian
Abstract

The objective of this paper is twofold: (a) to find a natural example of a perturbed Lagrangian that has different partial Noether operators with symmetries different from those of the underlying Lagrangian. First we regard the Schwarzschild spacetime as a perturbation of the Minkowski spacetime and investigate the approximate partial Noether operators for this perturbed spacetime. It is shown that the Minkowski spacetime has 12 partial Noether operators, 10 of which are different from the 17 Noether symmetries for this spacetime. It is found that for the perturbed Schwarzschild spacetime we recover the exact partial Noether operators as trivial first-order approximate partial Noether operators and there is no non-trivial approximate partial Noether operator as for the Noether case. As a consequence we state a conjecture. (b) Then we prove a conjecture that the approximate symmetries of a perturbed Lagrangian form a subalgebra of the approximate symmetries of the corresponding perturbed Euler–Lagrange equations and illustrate it by our examples. This is in contrast to approximate partial Noether operators.

Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - 1
Pages
13 - 25
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925110000556How to use a DOI?
Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Ibrar Hussain
AU  - F. M. Mahomed
AU  - Asghar Qadir
PY  - 2021
DA  - 2021/01
TI  - Approximate Partial Noether Operators of the Schwarzschild Spacetime
JO  - Journal of Nonlinear Mathematical Physics
SP  - 13
EP  - 25
VL  - 17
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000556
DO  - https://doi.org/10.1142/S1402925110000556
ID  - Hussain2021
ER  -