Abstract
The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature corresponding to the solutions obtained from the Ricci tensor of cylindrical spacetimes. Since these solutions are non-Minkowskian and are proposed to have curvature in almost all the cases, that is why some cylindrically symmetric static vacuum solutions of Einstein Field Equations have been worked out. We explore the Noether symmetries along with their conservation laws of the corresponding static-spacetime and calculate the equation of motions by taking into account Noether symmetries. We study the dynamics of particle in the form of effective potential, effective force.
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References
C W Misner, K S Thorne, J A Wheeler and W Gravitation Freeman and com- pany, San Francisco 891 (1973)
T Feroze, A Qadir and M Ziad J. Math. Phys. 42 4947 (2001)
A Qadir and M Ziad Il Nuovo Cimento B 110 277 (1995)
F Ali and T Feroze Int. J. Theor. Phys. 52 3329 (2013)
I A Khan et al., Int. J. Mod. Phys. D. 29 2050095 (2020)
F Ali and T Feroze Mathematics 4 50 (2016)
B P Abbott et al., Phys. Rev. Lett. 119 161101 (2017)
F Acernese et al., Classical. Quant. Grav. 32 024001 (2014)
M Soares-Santos et al., Astrophys. J. Lett. 848 L16 (2017)
C M Will Living reviews in relativity 17 4 (2014)
M Isi and A J Weinstein arXiv preprintarXiv:1710.03794 (2017)
T Callister et al., Phys. Rev. X 7 041058 (2017)
D N Spergel et al., Astrophys. J. Suppl 170 377 (2007)
Perlmutter et al., The Astrophys. J 517 565 (1999)
M Tegmark Phys. Rev. D. 69 103501 (2004)
U Seljak Phys. Rev. D. 71 103515 (2005)
M S Carroll Phys. Rev. Lett. 81 3067 (1998)
B Nayak and M Jamil Phys. Lett. B. 709 118 (2012)
C A Picon, V Mukhanov And J P Steinhard Phys. Rev. Lett. 85 4438 (2000)
D Kramer et al., Cambridge University Press(1980)
A S Khan and F Ali Phys. Dark. Universe. 100389 (2019)
G S Hall World Scientific, Singapore (2004)
P G Leach et al., J. Nonliear. Math. Phy. 8 139 (2001)
M Ali et al., Symmetry 11 4679 (2019)
A S Khan et al., Mod. Phys. lett. A. 30 2050234 (2020)
T Callister et al., Phy. Rev. X. 7 041058 (2017)
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Khan, I.A., Khan, A.S., Ali, F. et al. New cylindrically symmetric solution of Einstein field equations their conservation laws and the particles dynamics. Indian J Phys 96, 971–979 (2022). https://doi.org/10.1007/s12648-021-02014-3
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DOI: https://doi.org/10.1007/s12648-021-02014-3