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Search Results (5)

Search Parameters:
Keywords = static cylindrically symmetric spacetimes

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13 pages, 315 KiB  
Article
Killing Vector Fields of Static Cylindrically Symmetric Spacetime—A Rif Tree Approach
by Maryam Khalid Albuhayr, Ashfaque H. Bokhari and Tahir Hussain
Symmetry 2023, 15(5), 1111; https://doi.org/10.3390/sym15051111 - 19 May 2023
Viewed by 1812
Abstract
In this paper, we use an algebraic approach to classify cylindrically symmetric static spacetimes according to their killing vector fields. This approach is based on using a maple algorithm to re-cast the Killing’s equations into a reduced involutive form and integrating the Killing’s [...] Read more.
In this paper, we use an algebraic approach to classify cylindrically symmetric static spacetimes according to their killing vector fields. This approach is based on using a maple algorithm to re-cast the Killing’s equations into a reduced involutive form and integrating the Killing’s equations subject to the constraints given by the algorithm. It is shown that this approach provides some additional spacetime metrics, which were not provided previously by solving the Killing’s equations using a direct integration technique. To discuss some physical implications of the obtained spacetime metrics, we use them in the Einstein equations and discuss their significance. Full article
(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics)
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11 pages, 310 KiB  
Article
Noether Symmetries and Conservation Laws in Static Cylindrically Symmetric Spacetimes via Rif Tree Approach
by Muhammad Farhan, Suhad Subhi Aiadi, Tahir Hussain and Nabil Mlaiki
Symmetry 2023, 15(1), 184; https://doi.org/10.3390/sym15010184 - 8 Jan 2023
Cited by 3 | Viewed by 1586
Abstract
A new approach is adopted to completely classify the Lagrangian associated with the static cylindrically symmetric spacetime metric via Noether symmetries. The determining equations representing Noether symmetries are analyzed using a Maple algorithm that imposes different conditions on metric coefficients under which static [...] Read more.
A new approach is adopted to completely classify the Lagrangian associated with the static cylindrically symmetric spacetime metric via Noether symmetries. The determining equations representing Noether symmetries are analyzed using a Maple algorithm that imposes different conditions on metric coefficients under which static cylindrically symmetric spacetimes admit Noether symmetries of different dimensions. These conditions are used to solve the determining equations, giving the explicit form of vector fields representing Noether symmetries. The obtained Noether symmetry generators are used in Noether’s theorem to find the expressions for corresponding conservation laws. The singularity of the obtained metrics is discussed by finding their Kretschmann scalar. Full article
(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics)
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9 pages, 338 KiB  
Article
Homothetic Symmetries of Static Cylindrically Symmetric Spacetimes—A Rif Tree Approach
by Jamshed Khan, Tahir Hussain, Dania Santina and Nabil Mlaiki
Axioms 2022, 11(10), 506; https://doi.org/10.3390/axioms11100506 - 26 Sep 2022
Cited by 2 | Viewed by 1834
Abstract
In this paper, we find all static, cylindrically symmetric spacetime metrics admitting homothetic symmetries. For this purpose, first we analyze the homothetic symmetry equations by an algorithm developed in Maple which gives all possible static, cylindrically symmetric metrics that may possess proper homothetic [...] Read more.
In this paper, we find all static, cylindrically symmetric spacetime metrics admitting homothetic symmetries. For this purpose, first we analyze the homothetic symmetry equations by an algorithm developed in Maple which gives all possible static, cylindrically symmetric metrics that may possess proper homothetic symmetry. After that, we have solved the homothetic symmetry equations for all these metrics to get the final form of homothetic symmetry vector fields. Comparing the obtained results with those of direct integration technique, it is observed that the Rif tree approach not only recovers the metrics already found by direct integration technique, but it also produces some new metrics. Full article
(This article belongs to the Section Mathematical Physics)
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10 pages, 287 KiB  
Communication
Spinors in Cylindrically Symmetric Space–Time
by Bijan Saha
Universe 2020, 6(9), 152; https://doi.org/10.3390/universe6090152 - 15 Sep 2020
Cited by 5 | Viewed by 2257
Abstract
We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space–time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal components. The presence of non-diagonal components of the [...] Read more.
We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space–time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal components. The presence of non-diagonal components of the EMT imposes three-way restrictions either on the space–time geometry or on the components of the spinor field or on both. It should be noted that the analogical situation occurs in cosmology when the nonlinear spinor field is exploited as a source of gravitational field given by the Bianchi type-I cosmological model. Full article
(This article belongs to the Special Issue Selected Papers from the 17th Russian Gravitational Conference —International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17))
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15 pages, 283 KiB  
Article
Complete Classification of Cylindrically Symmetric Static Spacetimes and the Corresponding Conservation Laws
by Farhad Ali and Tooba Feroze
Mathematics 2016, 4(3), 50; https://doi.org/10.3390/math4030050 - 8 Aug 2016
Cited by 25 | Viewed by 3700
Abstract
In this paper we find the Noether symmetries of the Lagrangian of cylindrically symmetric static spacetimes. Using this approach we recover all cylindrically symmetric static spacetimes appeared in the classification by isometries and homotheties. We give different classes of cylindrically symmetric static spacetimes [...] Read more.
In this paper we find the Noether symmetries of the Lagrangian of cylindrically symmetric static spacetimes. Using this approach we recover all cylindrically symmetric static spacetimes appeared in the classification by isometries and homotheties. We give different classes of cylindrically symmetric static spacetimes along with the Noether symmetries of the corresponding Lagrangians and conservation laws. Full article
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