Semiconformal symmetry-A new symmetry of the space-time manifold of the general relativity
Volume 20, Issue 3, pp 241--254
http://dx.doi.org/10.22436/jmcs.020.03.07
Publication Date: February 12, 2020
Submission Date: October 04, 2019
Revision Date: November 27, 2019
Accteptance Date: December 12, 2019
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Authors
Naeem Ahmad Pundeer
- Department of Mathematics, Aligarh Muslim University, India.
Musavvir Ali
- Department of Mathematics, Aligarh Muslim University, India.
Naeem Ahmad
- Department of Mathematics, Unaizah Engineering College, Unaizah, Qassim University, Al-Qassim, KSA.
Zafar Ahsan
- Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, India.
Abstract
In this paper, we have introduced a new symmetry property of space-time which is named as semiconformal curvature collineation, and its relationship with other known symmetry properties has been established. This new symmetry property of the space-time has also been studied for non-null and null electromagnetic fields.
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ISRP Style
Naeem Ahmad Pundeer, Musavvir Ali, Naeem Ahmad, Zafar Ahsan, Semiconformal symmetry-A new symmetry of the space-time manifold of the general relativity, Journal of Mathematics and Computer Science, 20 (2020), no. 3, 241--254
AMA Style
Pundeer Naeem Ahmad, Ali Musavvir, Ahmad Naeem, Ahsan Zafar, Semiconformal symmetry-A new symmetry of the space-time manifold of the general relativity. J Math Comput SCI-JM. (2020); 20(3):241--254
Chicago/Turabian Style
Pundeer, Naeem Ahmad, Ali, Musavvir, Ahmad, Naeem, Ahsan, Zafar. "Semiconformal symmetry-A new symmetry of the space-time manifold of the general relativity." Journal of Mathematics and Computer Science, 20, no. 3 (2020): 241--254
Keywords
- Curvature tensor
- symmetries
- electromagnetic fields
MSC
References
-
[1]
Abdussattar, B. Dwivedi, On Conharmonic transformations in general relativity, Bull. Calcutta Math. Soc., 88 (1996), 465--470
-
[2]
Z. Ahsan, Collineation in electromagnetic fileds in general relativity-The null field case, Tamkang J. Math., 9 (1978), 237--240
-
[3]
Z. Ahsan, Symmetries of the electromagnetic fields in general relativity, Acta Phys. Sinica, 4 (1995), 337--343
-
[4]
Z. Ahsan, A symmetry property of the spacetime of general relativity in terms of space-matter tensor, Braz. J. Phys., 26 (1996), 572--576
-
[5]
Z. Ahsan, N. Ahsan, On a symmetry of the electromagnetic fields, Bull. Calcutta Math. Soc., 94 (2002), 385--388
-
[6]
Z. Ahsan, M. Ali, Symmetries of type $D$ pure radiation fields, Internat. J. Theoret. Phys., 51 (2012), 2044--2055
-
[7]
Z. Ahsan, M. Ali, Symmetries of Type N Pure Radiation Fields, Internat. J. Theoret. Phys., 54 (2015), 1397--1407
-
[8]
Z. Ahsan, M. Ali, Curvature tensor for spacetime of general relativity, Int. J. Geom. Methods Mod. Phys., 14 (2017), 13 pages
-
[9]
M. Ali, Z. Ahsan, Ricci solitons and symmetries of spacetime manifold of general relativity, Global J. Adv. Res. Classical Modern Geo., 1 (2012), 76--85
-
[10]
C. D. Collinson, Conservation laws in general relativity based upon existence of preferred collineation, Gen. Relativity Gravitation, 1 (1970/71), 137--142
-
[11]
K. L. Duggal, Existence of two Killing vector fieldson the spacetime of general relativity, Tensor (N. S.), 32 (1978), 318--322
-
[12]
L. P. Eisenhart, Riemannian Geometry, Princeton University Press, Princeton (1926)
-
[13]
Y. Ishii, On Conharmonic transformations, Tensor (N. S.), 7 (1957), 73--80
-
[14]
G. H. Katzin, J. Levine, W. R. Davis, Curvature collineation: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, J. Mathematical Phys., 10 (1969), 617--620
-
[15]
G. H. Katzin, J. Levine, W. R. Davis, Groups of curvature collineations in Riemannian space-times which admit fields of parallel vectors, J. Math. Phys., 11 (1970), 1578--1580
-
[16]
V. I. Khlebnikov, Gravitational radiation in electromagnetic universes, Classical Quantum Gravity, 3 (1986), 169--173
-
[17]
J. Kim, A type of conformal curvature tensor, Far East J. Math. Sci., 99 (2016), 61--74
-
[18]
J. Kim, On pseudo semiconformally symmetric manifolds, Bull. Korean Math. Soc., 54 (2017), 177--186
-
[19]
H. Michalaski, J. Wainwright, Killing vector fields and the Einstein-Maxwell field equations in general relativity, Gen. Relativity Gravitation, 6 (1975), 289--317
-
[20]
E. Newman, R. Penrose, An approach to gravitational radiation by a method of spin coefficients, J. Mathematical Phys., 3 (1962), 566--578
-
[21]
J. A. Schouten, Ricci Calculus: An Introduction to Tensor Analysis and its geometrical Applications, Springer-Verlag, Berlin-Göttingen-Heidelberg (1954)
-
[22]
A. A. Shaikh, S. K. Hui, On Weakly conharmonically symmetric manifolds, Tensor (N. S.), 70 (2008), 119--134
-
[23]
S. A. Siddiqui, Z. Ahsan, Conharmonic curvature tensor and the spacetime of General Relativity, Differ. Geom. Dyn. Syst., 12 (2010), 213--220
-
[24]
N. Tariq, B. O. J. Tupper, A class of algebraically general solutions of the Einstein-Maxwell equations for non-null electromagnetic field, Gen. Relativity Gravitation, 6 (1975), 345--360
-
[25]
T. Y. Thomas, The Differential Invariants of Generalized Spaces, Cambridge University Press, Cambridge (1934)
-
[26]
M. L. Woolley, The structure of groups of motions admitted by Einstein-Maxwell space-times, Comm. Math. Phys., 31 (1973), 75--81
-
[27]
K. Yano, Concircular Geometry I. Concircular Transformation, Proc. Imp. Acad. Tokyo, 16 (1940), 195--200
-
[28]
K. Yano, The Theory of Lie Derivatives and its Applications, North-Holland Publishing Co., Amsterdam (1957)
