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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 184, Number 1, Pages 92–105
DOI: https://doi.org/10.4213/tmf8846 (Mi tmf8846) 		 
This article is cited in 32 scientific papers (total in 32 papers)

Complete classification of spherically symmetric static space–times via Noether symmetries

F. Alia, T. Ferozea, S. Alib

a School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan
b School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad, Pakistan
Full-text PDF (384 kB) Citations (32)
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DOI: https://doi.org/10.4213/tmf8846
Abstract: We provide a complete classification of spherically symmetric static space–times by their Noether symmetries. We obtain the determining equations for the Noether symmetries using the usual Lagrangian of a general spherically symmetric static space–time and integrate them in each considered case. In particular, we find that spherically symmetric static space–times are categorized into six distinct classes corresponding to the Noether algebras of dimensions 5, 6, 7, 9, 11, and 17. Using Noether`s theorem, we also find the first integrals corresponding to each symmetry. Moreover, we obtain some new spherically symmetric static solutions.
Keywords: Noether symmetry, static space–time.
Received: 15.12.2014
Revised: 28.01.2015
English version:
Theoretical and Mathematical Physics, 2015, Volume 184, Issue 1, Pages 973–985
DOI: https://doi.org/10.1007/s11232-015-0310-2
Bibliographic databases:
Document Type: Article
MSC: PACS 11.30.-j-Symmetries and conservation laws, 04.20.-q-Classical general Relativity
Language: Russian
Citation: F. Ali, T. Feroze, S. Ali, “Complete classification of spherically symmetric static space–times via Noether symmetries”, TMF, 184:1 (2015), 92–105; Theoret. and Math. Phys., 184:1 (2015), 973–985
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v184/i1/p92
    • This publication is cited in the following 32 articles:
    1. F. Ali, M. Ali, Z. Shah, S. Iqbal, M. H. Alshehri, “Complete classification of static Bertotti–Robinson spacetime and its physical significance”, Indian J Phys, 98:4 (2024), 1545  crossref
    2. Jingli Fu, Yongxin Guo, Huidong Cheng, Fasheng Liu, Chen Yin, Zuoyuan Yin, “Lie symmetries and conserved quantities of static Bertotti–Robinson spacetime”, Chinese Journal of Physics, 89 (2024), 417  crossref
    3. Muhammad Saad Ghafar, Farhad Ali, Zahir Shah, Shahid Iqbal, Mansoor H. Alshehri, “Geodesic deviation analysis of time conformal Schwarzschild like black hole”, Indian J Phys, 2024  crossref
    4. Muhammad Farhan, Suhad Subhi Aiadi, Tahir Hussain, Nabil Mlaiki, “Noether Symmetries and Conservation Laws in Static Cylindrically Symmetric Spacetimes via Rif Tree Approach”, Symmetry, 15:1 (2023), 184  crossref
    5. Akram Mohammadpouri, Mir Sajjad Hashemi, Sona Samaei, “Noether symmetries and isometries of the area-minimizing Lagrangian on vacuum classes of pp-waves”, Eur. Phys. J. Plus, 138:2 (2023)  crossref
    6. Farhad Ali, Muhammad Saad Ghafar, Muhammad Atif Khan, Zahir Shah, “Approximate Noether symmetries of the geodetic Lagrangian of spherically symmetric spacetimes”, Eur. Phys. J. Plus, 138:3 (2023)  crossref
    7. Bokhari A.H., Farhan M., Hussain T., “Noether Symmetries of Bianchi Type i Spacetimes Via Rif Tree Approach”, Int. J. Geom. Methods Mod. Phys., 19:02 (2022), 2250030  crossref  mathscinet  isi
    8. Asghar Qadir, Ugur Camci, “Physical Significance of Noether Symmetries”, Symmetry, 14:3 (2022), 476  crossref
    9. Muhammad Farhan, Tahir Hussain, Fatima Azmi, Nabil Mlaiki, “Noether Symmetries and Conservation Laws in Non-Static Plane Symmetric Spacetime”, Symmetry, 14:10 (2022), 2174  crossref
    10. Muhammad Umair Shahzad, Hamood Ur Rehman, Aziz Ullah Awan, ElSayed M. Tag-ElDin, Attiq Ur Rehman, “Motion of Particles around Time Conformal Dilaton Black Holes”, Symmetry, 14:10 (2022), 2033  crossref
    11. M. Umair Shahzad, Abdul Jawad, Farhad Ali, G. Abbas, “Dynamics of particle near time conformal slowly rotating Kerr black hole”, Chinese Journal of Physics, 77 (2022), 620  crossref
    12. Muhammad Farhan, Tahir Hussain, Nabil Mlaiki, Aiman Mukheimer, “Noether Symmetries of Lemaitre-Tolman-Bondi Metric via Rif Tree Approach”, Symmetry, 14:9 (2022), 1864  crossref
    13. A. S. Khan, I. A. Khan, S. Islam, F. Ali, “Noether symmetry analysis for novel gravitational wave-like spacetimes and their conservation laws”, Mod. Phys. Lett. A, 35:28 (2020), 2050234  crossref  mathscinet  isi
    14. T. Hussain, S. S. Akhtar, A. H. Bokhari, “A study of energy conditions in non-static spherically symmetric spacetimes via Noether symmetries”, J. Math. Anal. Appl., 483:1 (2020), 123574  crossref  mathscinet  isi
    15. S. S. Akhtar, T. Hussain, “A study of Noether symmetries in lrs bianchi type V spacetimes”, Mod. Phys. Lett. A, 35:6 (2020), 2050026  crossref  mathscinet  isi
    16. F. Ali, M. A. Jan, W. Kh. Mashwani, R. A. Khanum, H. U. Khan, “The physical significance of time conformal Minkowski spacetime”, Mehran Univ. Res. J. Eng. Technol., 39:2 (2020), 365–370  crossref  isi
    17. I. A. Khan, F. Ali, S. Islam, A. S. Khan, “The role of the cosmological constant in dynamics of the particle in the Schwarzschild black hole”, Phys. Scr., 95:6 (2020), 065003  crossref  mathscinet  isi
    18. A. S. Khan, F. Ali, “Dynamics of particles around the time conformal quantum corrected Schwarzschild black hole”, Phys. Dark Universe, 30 (2020), 100714  crossref  isi
    19. S. S. Akhtar, T. Hussain, “Energy conditions and conservation laws in lrs bianchi type i spacetimes via Noether symmetries”, Commun. Theor. Phys., 71:3 (2019), 298–306  crossref  mathscinet  isi  scopus
    20. M. Ali, F. Ali, A. Saboor, M. S. Ghafar, A. S. Khan, “The second-order correction to the energy and momentum in plane symmetric gravitational waves like spacetimes”, Symmetry-Basel, 11:2 (2019), 220  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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