Approximate Partial Noether Operators of the Schwarzschild Spacetime

DOI

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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TY  - JOUR
AU  - Ibrar Hussain
AU  - F. M. Mahomed
AU  - Asghar Qadir
PY  - 2021
DA  - 2021/01/07
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  - 10.1142/S1402925110000556
ID  - Hussain2021
ER  -