A WEAK GRAVITATIONAL KNOT IN (2+1)-DIMENSIONAL EMPTY SPACE-TIME
DOI:
10.29303/ipr.v8i1.346Downloads
Abstract
We propose the existence of a topological object, a weak gravitational knot, in the framework of an Abelian Chern-Simons action with a small positive cosmological constant in (2+1)-dimensional empty space-time.
Keywords:
(2 1) gravity theory, empty space-time, cosmological constant, weak-field limit, Abelian Chern-Simons action, gravitational knotReferences
Antonio F Ranada, “Topological electromagnetismâ€, J. Phys. A: Math. Gen. 25 (1992) 1621-1641.
Chen Ning Yang, “Topology and Gauge Theory in Physicsâ€, International Journal of Modern Physics A, Vol. 27, No. 30 (2012) 1230035.
Y. M. Cho, “Gauge theory, gravitation, and symmetryâ€, Physical Review D, Volume 14, Number 12, 15 December 1976. Y. M. Cho, “Einstein Lagrangian as the translational Yang-Mills Lagrangianâ€, Physical Review D, Volume 14, Number 10, 15 November 1976.
Edward Witten, “2+1 Dimensional Gravity as an Exactly Soluble Systemâ€, Nuclear Physics B 311 (1988) 46-78. 5
Steven Carlip, “Quantum Gravity in 2+1 Dimensionsâ€, Cambridge University Press, 2003.
Bastian Wemmenhove, “Quantisation of 2+1 dimensional Gravity as a Chern-Simons theoryâ€, Thesis, Instituut voor Theoretische Fysica, Amsterdam, 2002.
Wouter Merbis, “Chern-Simons–like Theories of Gravityâ€, Ph.D. Thesis, University of Groningen, 2014.
Roman Jackiw, “Diverse Topics in Theoretical and Mathematical Physicsâ€, World Scientific, 1995.
Roman Jackiw, “Lower Dimensional Gravityâ€, Nuclear Physics B 252 (1985) 343-356.
Jorge Zanelli, “Chern-Simons Gravity: From 2+1 to 2n+1 Dimensionsâ€, Brazilian Journal of Physics, Vol. 30, No.2, June 2000.
A. V. Crisan, C. R. L. Godinho, I. V. Vancea, “Gravitoelectromagnetic knot fieldsâ€, arXiv:2103.00217v1 [gr-qc] 27 Feb 2021
Y. M. Cho, Seung Hun Oh, Pengming Zhang, “Knots in Physicsâ€, International Journal of Modern Physics A, Vol. 33, No. 07, 1830006 (2018).
Y. M. Cho, Franklin H. Cho and J.H. Yoon, “Vacuum decomposition of Einstein’s theory and knot topology of vacuum space-timeâ€, Class. Quantum Grav. 30 (2013) 055003 (17pp).
Michael Atiyah, “The Geometry and Physics of Knotsâ€, Cambridge University Press, 1990.
Ji-rong Ren, Ran Li, Yi-shi Duan, “Inner topological structure of Hopf invariantâ€, https://arxiv.org/abs/0705.4337v1, 2007.
Yi-shi Duan, Xin Liu, Li-bin Fu, “Many knots in Chern-Simons field theoryâ€, Physical Review D 67, 085022 (2003).
Antonio F. Ranada, “A Topological Theory of the Electromagnetic Fieldâ€, Letters in Mathematical Physics 18: 97-106, 1989.
P. A. M. Dirac, “General Theory of Relativityâ€, John Wiley & Sons, 1975.
K. Surya Kiran, Chethan Krishnan, Avinash Raju, “3D Gravity, Chern-Simons and Higher Spins: A Mini Introductionâ€, arXiv:1412.5053v3 [hep-th] 15 Sep 2015.
Manfredo P. do Carmo, “Differential Geometry of Curves and Surfacesâ€, Prentice Hall Inc., 1976.
Mark Srednicki, “Quantum Field Theoryâ€, Cambridge University Press, 2007.
James B. Hartle, “Gravity: An Introduction to Einstein’s General Relativityâ€, Pearson, 2014.
Miftachul Hadi, “Knot in weak-field geometrical opticsâ€, OSF, https://osf.io/e7afj/, 2023, and all references therein.
A. F. Ranada, A. Tiemblo, “A Topological Structure in the Set of Classical Free Radiation Electromagnetic Fieldsâ€, arXiv:1407.8145v1 [physics.class-ph] 29 Jul 2014.
Roman Jackiw, “Lectures on Fluid Dynamicsâ€, Springer, 2002.
Miftachul Hadi, Hans Jacobus Wospakrik, “SU(2) Skyrme Model for Hadronâ€, https://arxiv.org/abs/1007.0888, 2010.
Miftachul Hadi, Irwandi Nurdin, Denny Hermawanto, “Analytical Analysis and Numerical Solution of Two Flavours Skyrmionâ€, https://arxiv.org/abs/1006.5601, 2010.
J. H. C. Whitehead, “An Expression of Hopf’s Invariant as an Integralâ€, Proceedings of the National Academy of Sciences, Vol. 33, No. 5, 117-123, 1947.
Raoul Bott, Loring W. Tu, “Differential Forms in Algebraic Topologyâ€, Springer, 1982.
John Baez, Javier P. Muniain, “Gauge Fields, Knots and Gravityâ€, World Scientific, 1994.
M.P. Hobson, G.P. Efstathiou, A.N. Lasenby, “General Relativity: An Introduction for Physicistsâ€, Cambridge University Press, 2006.
Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, “Gravitationâ€, W. H. Freeman and Company, 1973.
Amy Thompson, Alexander Wickes, Joe Swearngin, Dirk Bouwmeester, “Classification of Electromagnetic and Gravitational Hopfions by Algebraic Typeâ€, arXiv:1411.2073v2 [gr-qc] 2 May 2015.
Miftachul Hadi, “On Newtonian knot in (2+1)-dimensional empty space-timeâ€, OSF, https: //osf.io/preprints/osf/su3dp, 2024, and all references therein
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors who publish with Indonesian Physical Review Journal, agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-ShareAlike 4.0 International Licence (CC BY SA-4.0). This license allows authors to use all articles, data sets, graphics, and appendices in data mining applications, search engines, web sites, blogs, and other platforms by providing an appropriate reference. The journal allows the author(s) to hold the copyright without restrictions and will retain publishing rights without restrictions.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in Indonesian Physical Review Journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
