Noether symmetries and conservation laws of wave equation on static spherically symmetric spacetimes with higher symmetries

2015 ◽  
Vol 23 (1-3) ◽  
pp. 141-152 ◽  
Author(s):  
M.T. Mustafa ◽  
Ahmad Y. Al-Dweik
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Spherically Symmetric ◽  
Noether Symmetries ◽  
Higher Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes

Classification of Static Spherically Symmetric Spacetimes by Noether Symmetries

2013 ◽  
Vol 52 (10) ◽  
pp. 3534-3542 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
A. G. Johnpillai ◽  
A. H. Kara ◽  
F. M. Mahomed ◽  
F. D. Zaman
Keyword(s):  
Spherically Symmetric ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes

Conservation laws corresponding to the Noether symmetries of the geodetic Lagrangian in spherically symmetric spacetimes

2017 ◽  
Vol 26 (05) ◽  
pp. 1741006 ◽  
Author(s):  
Bismah Jamil ◽  
Tooba Feroze
Keyword(s):  
Conservation Laws ◽  
Noether Symmetry ◽  
Complete List ◽  
Spherically Symmetric ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes

In this paper, we present a complete list of spherically symmetric nonstatic spacetimes along with the generators of all Noether symmetries of the geodetic Lagrangian for such metrics. Moreover, physical and geometrical interpretations of the conserved quantities (conservation laws) corresponding to each Noether symmetry are also given.

scholarly journals Invariant Solutions of the Wave Equation on Static Spherically Symmetric Spacetimes Admitting G7 Isometry Algebra

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 665 ◽  
Author(s):  
Hassan Azad ◽  
Khaleel Anaya ◽  
Ahmad Al-Dweik ◽  
M. Mustafa
Keyword(s):  
Wave Equation ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Algebra Structure ◽  
Spherically Symmetric ◽  
Invariant Solutions ◽  
Symmetric Spacetimes ◽  
Joint Invariants ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes

Algorithms to construct the optimal systems of dimension of at most three of Lie algebras are given. These algorithms are applied to determine the Lie algebra structure and optimal systems of the symmetries of the wave equation on static spherically symmetric spacetimes admitting G7 as an isometry algebra. Joint invariants and invariant solutions corresponding to three-dimensional optimal systems are also determined.

scholarly journals Bondi accretion in the spherically symmetric Johannsen–Psaltis spacetime

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Anslyn J. John ◽  
Chris Z. Stevens
Keyword(s):  
Accretion Rate ◽  
Kerr Metric ◽  
Spherically Symmetric ◽  
Gravitational Acceleration ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes ◽  
Scalar Hair ◽  
Relativistic Analysis ◽  
Modified Theory ◽  
Static Spherically Symmetric Spacetimes

AbstractThe Johannsen–Psaltis spacetime explicitly violates the no-hair theorem. It describes rotating black holes with scalar hair in the form of parametric deviations from the Kerr metric. In principle, black hole solutions in any modified theory of gravity could be written in terms of the Johannsen–Psaltis metric. We study the accretion of gas onto a static limit of this spacetime. We utilise a recently proposed pseudo–Newtonian formulation of the dynamics around arbitrary static, spherically symmetric spacetimes. We obtain a potential that generalises the Paczyński–Wiita potential to the static Johannsen–Psaltis metric. We also perform a fully relativistic analysis of the geodesic equations in the static Johannsen–Psaltis spacetime. We find that positive (negative) values of the scalar hair parameter, $$\epsilon _{3}$$ϵ3, lower (raise) the accretion rate. Similarly, positive (negative) values of $$\epsilon _{3}$$ϵ3 reduce (increase) the gravitational acceleration of radially infalling massive particles.

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