Teleparallel Killing Vectors of the Einstein Universe

Sharif, M.; Amir, M. Jamil

doi:10.1142/s0217732308025474

Cited by 36 publications

(30 citation statements)

References 29 publications

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“…Otherwise, these expressions gave a non physical results. • To make the picture more clear we have calculated the Killing vectors associated with these tetrad fields using the definition of the Lie derivative of a second rank tensor in the framework of TEGR (Sharif and Jamil 2008). We have shown by explicit calculations that the tetrad field which shows consistent results of energy, irreducible mass, momentum and angular momentum continue to show consistency for the Killing vector with GR.…”

Section: Main Results and Discussionmentioning

confidence: 99%

“…In this section, we are going to calculate the Killing vectors of the Schwarzschild space-times using the teleparallel Lie derivatives of a covariant tensor (Sharif and Jamil 2008) which is defined as…”

Section: Teleparallel Killing Vectors Of the Schwarzschild Space-timesmentioning

confidence: 99%

“…We use the definition of energy-momentum tensor and angular momentum tensor which is coordinate independent, of the gravitational field established in the Hamiltonian structure of TEGR to calculate energy, spatial momentum and angular momentum. We also calculate the Killing vectors associated with these tetrads using the teleparallel version of the Lie derivative (Sharif and Jamil 2008).…”

Section: Introductionmentioning

confidence: 99%

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Killing vectors of Schwarzschild space-times in teleparallel equivalent of general relativity

Nashed

2011

Astrophys Space Sci

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Section: Main Results and Discussionmentioning

confidence: 99%

Section: Teleparallel Killing Vectors Of the Schwarzschild Space-timesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Killing vectors of Schwarzschild space-times in teleparallel equivalent of general relativity

Nashed

2011

Astrophys Space Sci

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“…M. Sharif et. al [13] introduced the concept of Killing symmetry in teleparallel theory and they got Killing vector fields for the Einstein space. In general relativity Killing vector fields are considered as an essential symmetry.…”

mentioning

confidence: 99%

Killing Symmetry in Special Axially Symmetric Static Spacetimes in Teleparalel Theory of Gravitation

Khan¹

2015

VFAST trans. math.

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1. Introduction. The importance of symmetry in both the theory of general relativity and teleparallel theory of gravitation is pretty clear as many physical laws in the universe are direct applications of symmetry in all types of relativity theories, that is in special, general and teleparallel theory of gravitation. Many researchers made their contributions in different types of symmetry and found a lot of hidden information of the universe by using different models of symmetry. Actually Einstein field equations give a relation between geometry and physics of the universe and symmetries play a vital role in the classification of solutions of Einstein field equations. Symmetry limitations are extremely supportive. During the last three decades, a lot of concentration has been given to the knowledge of different types of symmetries. One feature that helps us to recognize and expose the unseen realities of the space is the knowledge of conservation laws of a spacetime for the metric. As the conservation laws are attainable from the symmetry of spacetime [1], Killing, homothetic, conformal Killing and self similar symmetries of a spacetimes are extensively studied in the existence of curvature [2][3][4][5][6][7][8][9][10][11]. It has been noticed in the earlier period that for the spacetime having torsion only, the law of gravitation can be equally described [12]. M. Sharif et. al [13] introduced the concept of Killing symmetry in teleparallel theory and they got Killing vector fields for the Einstein space. In general relativity Killing vector fields are considered as an essential symmetry. In the background of teleparallel theory, a lot of work has been finished in obtaining Killing vector fields for different spacetimes [14][15][16][17][18][19][20][21][22]. To understand the physical and geometrical feature of our unexplained universe, much work is required to be done through symmetries in the presence of curvature or torsion only.

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“…In the past it has been observed that the laws of gravitation can be equivalently described for the spacetime having torsion only [12]. The idea of Killing symmetry in teleparallel theory was introduced by M. Sharif et al [13]. They obtained Killing vectors for Einstein universe in the presence of torsion only.…”

mentioning

confidence: 99%